Treatment of vowel harmony in optimality theory

Treatment of vowel harmony in optimalitytheorySasa, Tomomasahttps://iro.uiowa.edu/discovery/delivery/01IOWA_INST:ResearchRepository/12730570670002771?l#13730728520002771

Sasa. (2009). Treatment of vowel harmony in optimality theory [University of Iowa].https://doi.org/10.17077/etd.v67d44xx

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TREATMENTS OF VOWEL HARMONY IN OPTIMALITY THEORY

Tomomasa Sasa

An Abstract

Of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Linguistics

in the Graduate College of The University of Iowa

July 2009

Thesis Supervisors: Professor Catherine Ringen

Associate Professor Jill Beckman

ABSTRACT

From the early stage of Optimality Theory (OT) (Prince, Alan and Paul

Smolensky (1993): Optimality Theory: Constraint Interaction in Generative Grammar.

[ROA: 537-0802: http://roa.rutgers.edu], McCarthy, John J. and Alan Prince

(1995). Faithfulness and reduplicative identity. In Jill Beckman, Laura W. Dickey

and Suzanne Urbanczyk (eds.) Papers in Optimality Theory. Amherst, MA: GLSA.

249-384), a number of analyses have been proposed to account for vowel

harmony in the OT framework. However, because of the diversity of the

patterns attested cross-linguistically, no consensus has been reached with regard

to the OT treatment of vowel harmony. This, in turn, raises the question whether

OT is a viable phonological theory to account for vowel harmony; if a theory is

viable, a uniform account of the diverse patterns of vowel harmony should be

possible.

The main purpose of this thesis is to discuss the application of five

different OT approaches to vowel harmony, and to investigate which approach

offers the most comprehensive coverage of the diverse vowel harmony

patterns. Three approaches are the main focus: feature linking with SPREAD

(Padgett, Jaye (2002). Feature classes in phonology. Language 78. 81-110),

Agreement-By-Correspondence (ABC) (Walker, Rachel (2009). Similarity-

sensitive blocking and transparency in Menominee. Paper presented at the 83rd

Annual Meeting of the Linguistic Society of America. San Francisco), and the

Span Theory of harmony (McCarthy, John J. (2004). Headed spans and

autosegmental spreading. [ROA: 685-0904: http://roa.rutgers.edu]). The

applications of these approaches in the following languages are considered:

backness and roundness harmony in Turkish and in Yakut (Turkic), and ATR

harmony in Pulaar (Niger-Congo). It is demonstrated that both feature linking

and ABC analyses are successful in offering a uniform account of the different

types of harmony processes observed in these three languages. However, Span

Theory turns out to be empirically inadequate when used in the analysis of

Pulaar harmony. These results lead to the conclusion that there are two

approaches within OT that can offer a uniform account of the vowel harmony

processes. This also suggests that OT is viable as a phonological theory.

Abstract Approved: !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " " Thesis Supervisor !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " " Title and Department !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " " Date !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " " Thesis Supervisor !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " " Title and Department !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " " Date!

TREATMENTS OF VOWEL HARMONY IN OPTIMALITY THEORY

Tomomasa Sasa

A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Linguistics in the Graduate College of

The University of Iowa

July 2009

Thesis Supervisors: Professor Catherine O. Ringen Associate Professor Jill Beckman

Graduate College The University of Iowa

Iowa City, Iowa

CERTIFICATE OF APPROVAL !!!!!!!!!!!!!!!!!!!!!!!!!!!!"

PH.D. THESIS !!!!!!!!!!!!!"

This is to certify that the Ph.D. thesis of

Tomomasa Sasa

has been approved by the Examining Committee for the thesis requirement for the Doctor of Philosophy degree in Linguistics at the July 2009 graduation. Thesis Committee: !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Catherine O. Ringen, Thesis Co-supervisor !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " Jill Beckman, Thesis Co-supervisor !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " Jerzy Rubach !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " William D. Davies !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"

" " " " " Bob McMurray

To my family and friends

! """!

ACKNOWLEDGEMENTS

“Why are you doing phonology?” I have been asked this question a

number of times during my time in graduate school. I would like to use this

opportunity to answer this question; my answer, simply, is that I am a

phonologist because I had the opportunities to meet and work with some

fascinating people, who otherwise I would have not met.

First, this thesis would never have been possible without the tremendous

support of Professors Catherine Ringen and Jill Beckman; no words are sufficient

for me to describe how impressive they are. I was always touched by their

generous support for me throughout the thesis-writing process, and with other

academic matters.

Professor Jerzy Rubach taught me the excitement and reality of

phonology; all of his words are deeply rooted in me, and they built up the

foundation of my thinking, reasoning, and teaching in phonology. Professor

William D. Davies taught me the dynamism of human languages (that is, how

messy languages are), and gave me a valuable lesson that no linguistic theory is

viable if we overlook the data. Professor Bob McMurray never failed to impress

me with his broad and in-depth knowledge, interest, and enthusiasm.

I would also like to express my thanks to my fellow graduate students in

the Linguistics Department: Dr. Ivan Ivanov (Ivancho), Dr. Marta Tryzna, and

Dr. Kumyoung Lee, with whom I shared both good and hard times in the past

five years. I will never forget about the encouragement and support from the

following friends of mine: Michael Bortscheller (Borts), Lalita Dhareshwar,

Lauren Eby, Jane Gressang, Zachary Harper, Sangkyun Kang (Danny), Molly

Kelley, Vladimir Kulikov (Volodya), Eri Kurniawan, Jeffery Press, Lindsey

Quinn-Wriedt, Jaeyoung Shim, Mano Yasuda, and Dr. Roberto Mayoral

Hernández.

Finally (but never least), I would like to express my very special gratitude

to Professor Rachel Walker at USC, and Ms. Barbara Hermeier, the former

secretary in the Linguistics Department. My research, teaching, and mentoring

have been significantly influenced by Professor Walker’s; from her, I learned to

be open-minded to the suggestions, critiques, and new proposals. My very

special thanks also go to Ms. Hermeier; my life in the United States was

impossible without her support; she always went out of her way to help me and

other graduate students in the Linguistics Department.

I would like to thank these above mentioned people for their support,

suggestions, critiques, and encouragement, which all made this thesis possible.

Nonetheless, all mistakes, including the improper usage of commas and the

lack/overuse of determiners, are mine.

TABLE OF CONTENTS

LIST OF TABLES............................................................................................................. vii LIST OF FIGURES.......................................................................................................... viii CHAPTER I AN OPTIMALITY-THEORETIC TREATMENT OF VOWEL HARMONY: AN OVERVIEW...............................1 1.1 A Survey of the Harmony Patterns .............................................................3 1.2 An Optimality-Theoretic Account of Vowel Harmony...........................10 1.2.1 Feature Alignment.........................................................................10 1.2.2 Feature Linking with Spread........................................................22 1.2.3 Local Agree .....................................................................................26 1.2.4 Summary.........................................................................................31 1.3 Recent Developments: An Overview ........................................................33 1.3.1 Span Theory ...................................................................................33 1.3.2 Agreement By Correspondence (ABC)......................................38 1.4 The Organization of the Thesis ..................................................................43 CHAPTER II TURKISH VOWEL HARMONY: A CASE STUDY .................45 2.1 Turkish Vowel Harmony.............................................................................45 2.2 The Feature Linking Analysis .....................................................................48 2.3 The ABC Analysis .........................................................................................55 2.4 The Span-Theoretic Analysis .......................................................................61 2.4.1 Span-Theoretic Constraints ..........................................................62 2.4.2 The Analysis....................................................................................69 2.5 Discussion.......................................................................................................72 2.5.1 Accounting for Two Harmony Processes ..................................72 2.5.2 Disharmonic Roots.........................................................................75 2.5.3 Summary of the Chapter ..............................................................78 CHAPTER III HARMONY PATHOLOGIES: SOUR GRAPES IN PULAAR ATR HARMONY......................79 3.1 Pulaar Data.....................................................................................................80 3.2 Empirical Issues .............................................................................................84 3.2.1 Sour Grapes.....................................................................................85

3.2.2 Directionality...................................................................................88 3.3 Span Theory and Privative [ATR]...............................................................90 3.4 Span Theory and Binary [ATR].................................................................104 3.5 Discussion.....................................................................................................109

CHAPTER IV PULAAR ATR HARMONY: FULL ANALYSES WITH SPREAD AND ABC......................113 4.1 Review of the Pulaar Data .........................................................................113 4.2 Analysis with Spread ..................................................................................116 4.2.1 Spread Defined .............................................................................116 4.2.2 The Analysis with Spread-Left ...................................................121 4.3 The ABC Analysis........................................................................................131 4.4 General Discussion......................................................................................145 4.4.1 Positional Faithfulness in Harmony .........................................145 4.4.2 Privative [ATR].............................................................................148 4.4.3 Summary.......................................................................................155 CHAPTER V ROUNDNESS HARMONY REVISITED: A CASE STUDY OF YAKUT....................................................157 5.1 Yakut Roundness Harmony......................................................................157 5.2 The Analysis with Spread...........................................................................164 5.2.1 Roundness Harmony ..................................................................164 5.2.2 Backness Harmony......................................................................174 5.3 Agreement By Correspondence...............................................................175 5.3.1 The ABC Analysis of Yakut Roundness Harmony.................176 5.3.2 The ABC Account of Yakut Backness Harmony.....................184 5.4 Discussion.....................................................................................................189 5.4.1 Summary of the Chapter ............................................................189 5.4.2 A Residual Issue............................................................................190 CHAPTER VI ISSUES IN THE OT TREATMENT OF VOWEL HARMONY ................................................................198

6.1 Summary......................................................................................................198 6.2 On the Constraint Spread ..........................................................................201 6.3 Harmony Pathology Revisited .................................................................205 6.4 Conclusion....................................................................................................213 REFERENCES ................................................................................................................215

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LIST OF TABLES

Table 1 Predictions under Align, Spread, and Agree.......................................32 Table 2 Turkish Vowel Inventory ......................................................................46 Table 3 Restrictions on Roundness Harmony in Turkish...............................48 Table 4 The Evaluation by the Original *A-Span [round] ..............................65 Table 5 Satisfaction and Violation of S-Parse....................................................66 Table 6 Pulaar Vowel Inventory.........................................................................80 Table 7 The Evaluation of Id VV [ATR]...........................................................154 Table 8 Vowel Inventory of Yakut...................................................................158 Table 9 Yakut Diphthongs.................................................................................159 Table 10 Restrictions on Roundness Harmony in Yakut................................163 Table 11 Restrictions on Roundness Harmony in Kachin Khakass ..............191 Table 12 Summary of the Analyses....................................................................199

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LIST OF FIGURES

Figure 1 Schematic Representations of Vowel Harmony ..................................3 Figure 2 A Gapped Configuration .......................................................................11 Figure 3 Evaluation under Agree 1......................................................................26 Figure 4 Evaluation under Agree 2......................................................................27 Figure 5 Correspondence in ABC ........................................................................39 Figure 6 ABC Ranking for Harmony ..................................................................42 Figure 7 Ranking Lattice: Turkish/Spread..........................................................54 Figure 8 Ranking Lattice: Turkish/ABC..............................................................60 Figure 9 Ranking Lattice: Turkish/Span Theory ...............................................71 Figure 10 Ranking Lattice: Pulaar/Span Theory..................................................99 Figure 11 Satisfaction and Violation of Spread 1................................................119 Figure 12 Satisfaction and Violation of Spread 2................................................120 Figure 13 Configurations of (14a) and (14b).......................................................125 Figure 14 Ranking Lattice: Pulaar/Spread..........................................................130 Figure 15 Ranking Lattice: Pulaar/ABC..............................................................143 Figure 16 The Evaluation of *High-Low [round]...............................................169 Figure 17 Ranking Lattice: Yakut/Spread...........................................................172 Figure 18 Ranking Lattice: Yakut/ABC...............................................................182

CHAPTER I AN OPTIMALITY-THEORETIC TREATMENT OF VOWEL HARMONY:

AN OVERVIEW Vowel harmony, a phonological phenomenon in which vowels in a

certain domain (such as ‘a word’) agree with a certain vowel (such as ‘a vowel in

the first syllable’ or ‘a vowel with a certain feature specification’) has been

extensively discussed both in Optimality Theory (OT) (Prince and Smolensky

1993, McCarthy and Prince 1995) and in pre-OT frameworks. In the OT

framework, several approaches have been proposed to account for the diverse

patterns of vowel harmony that are found cross-linguistically. The earlier

approaches include i) feature alignment (Kirchner 1993), ii) local agreement (cf.

Bakovic 2000), and iii) feature spreading (Padgett 1997, 2002). Some of the more

recent treatments of vowel harmony include the Span Theory of harmony

(McCarthy 2004, Smolensky and Legendre 2006), and Agreement-By-

Correspondence (ABC) (Rose and Walker 2004, Walker 2009).

However, a very fundamental question remains unanswered: what is the

most comprehensive and uniform way to account for the diverse vowel

harmony patterns observed cross-linguistically? Even though numerous studies

have been proposed within different OT frameworks, there is no consensus with

regard to how vowel harmony should be treated in OT. In fact, none of the

previous approaches has been shown to be empirically sufficient to account for

the diverse vowel harmony patterns. This leads us to address another question:

is OT able to provide comprehensive analyses of vowel harmony?

There are two main goals of this thesis; first, I investigate whether OT is

viable as a phonological theory to account for the diverse vowel harmony

patterns observed cross-linguistically. To answer this question, I present an

empirical comparison of the different frameworks that have been proposed to

account for harmony. Second, I address the question of which framework, if any,

offers the most comprehensive coverage of the attested vowel harmony

patterns. In addition to these main questions, I discuss the theoretical issues that

arise through the investigations of the harmony patterns and in the examination

of each different approach with the attested vowel harmony data.

The following five different approaches are considered in the thesis: i)

feature alignment, ii) local agreement, iii) feature linking, iv) Span Theory, and v)

Agreement-By-Correspondence. However, as will be demonstrated in this

chapter, two of the approaches, i) feature alignment and ii) local agreement, are

eliminated for theoretical or empirical reasons. Thus, this thesis mainly discusses

the remaining three approaches, iii) feature linking, iv) Span Theory, and v) ABC

with data from the following languages: Turkish (backness and roundness

harmony), Pulaar (ATR harmony with directionality and opacity), and Yakut

(backness harmony and the blocking effect in roundness harmony).

The organization of this chapter is as follows; Section 1.1 is a presentation

of a survey of vowel harmony patterns, and it introduces four patterns: total

harmony, opacity, transparency, and dominant-recessive. In Section 1.2, the

overview of three approaches, feature alignment, local agreement, and feature

linking is presented. In Section 1.3, I present an overview of the Span-Theoretic

approach and the ABC approach to vowel harmony.

1.1 A Survey of the Harmony Patterns

Both in Optimality Theoretic (OT) and pre-OT frameworks, various types

of harmony have been described in great detail. The schematic representations in

Figure 1 present some of the harmony patterns commonly observed cross-

linguistically; the pattern in (a) is referred to as total harmony, (b) is referred to

as opacity, and (c) is referred to as transparency.

(a) V1 V2 V3

!"! !"! !"! [! F] [! F] [! F] (b) V1 V2 V3

!"! !"! !"! [! F] [" F] [" F] (c) V1 V2 V3

!"! !"! !"! [! F] [" F] [! F] Figure 1. Schematic Representations of Vowel Harmony (a) Total harmony (b) Opacity (c) Transparency There is one more commonly attested harmony pattern, namely, dominant-

recessive, in addition to (a) through (c) in Figure 1. The dominant-recessive data

from Diola-Fogny (Sapir 1965) are presented later in this section.

In accounting for harmony (both in OT and pre-OT frameworks), the

terms trigger and target are frequently used; the term trigger refers to a vowel

with which all other vowels agree in (a) certain feature(s). The term target refers

to the vowel(s) which agree(s) with the trigger in a harmony domain; targets

harmonize with the trigger. In the schematic representation in Figure 1, let the

leftmost vowel (labeled as V1) be the trigger of the harmony, and let V2 and V3

be the targets of the harmony. In Figure 1, the feature [F] represents any feature

(for example, backness, roundness, or [ATR]), and the Greek letters ! and " refer

to different values for the feature [F].

The representation presented in (a) in Figure 1 is referred to as total

harmony. In total harmony, all the vowels in a domain agree with the trigger. For

example, this harmony pattern is observed in the backness harmony in Yakut, a

Turkic language spoken in Siberia.

(1) Yakut Backness Harmony (Krueger 1962: 72-75, 80-82)

Plural Accusative

a. kinige kinige-ler kinige-ni ‘book’

b. a©a a©a-lar a©a-n! ‘father’

In Yakut backness harmony, all the vowels in a word agree with the root-initial

vowel for backness. For example, in (1a), both the plural and the accusative

suffixes contain a [-back] vowel because the first vowel in the root is [-back]. In

(1b), the suffixes contain a [+back] vowel because of the [+back] vowels in the

root. In backness harmony, all the vowels in a domain agree in backness (or

share the same backness feature). One of the characteristics of total harmony,

which differentiates this pattern from dominant-recessive, is that total harmony

is triggered by a vowel in a privileged position; for example, in Yakut backness

harmony, the vowel in the first syllable of a word triggers harmony. As will be

shown, in a dominant-recessive system, a vowel with a certain specification

triggers harmony regardless of the position of the vowel.1

The second type of harmony, as represented in (b) in Figure 1, contains an

opaque vowel. In such a system, the vowel adjacent to the trigger (in (b) of Figure

1, the vowel labeled as V2) does not agree with the trigger of the harmony. In

addition, in (b) of Figure 1, the final vowel, which is labeled as V3, agrees with the

intervening vowel, not the trigger of the harmony, for the feature [F]. The data

in (2) illustrate the opaque behavior of the low vowel [a] in Pulaar [ATR]

harmony, where the trigger of [ATR] harmony is the vowel in the final syllable

of a word. That is, the directionality of the harmony is from right to left, and the

harmony pattern observed in Pulaar is the mirror image of the schematic

representation in (b) of Figure 1.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 Privileged positions refer to the positions that are more prominent compared

with other positions; for example, presonorant (a position before a sonorant segment) is considered to be prominent (cf. Lombardi 1999, Petrova et al. 2006), and the first syllable of a word is also assumed to be prominent (cf. Beckman 1997, 1998). Morphological roots are considered to be more prominent than affixes (McCarthy and Prince 1995).

(2) Pulaar Low Vowel Opacity (Paradis 1992: 88, as cited in Kra‹mer 2001: 122)

a. bø…t-a…-ri ‘lunch’ (*bo…t-aa-ri)

b. pø…f-a…-li ‘breaths’ (*po…f-a…-ri)

c. nødd-a…-li ‘call’ (*nodd-a…-ri)

d. ˜gør-a…-gu ‘courage’ (*˜gor-a…-gu)

cf. e) be…l-i ‘puddles-class’ b´…l-øn ‘puddles-dim.pl’

In Pulaar, the vowels [i, e] are specified as [+ATR] and [ˆ, ´, a] are specified

as [-ATR]. The vowel [a] is specified as [+low, -ATR]. In Pulaar, there is no [+low,

+ATR] vowel, and thus, [a] never alternates in its [ATR] specification, even when

it is followed by a [+ATR] vowel. In [ATR] harmony, all the vowels in a word

agree with the rightmost vowel (the vowel in the final syllable) in specification

for [ATR]. In the forms in (2), since the last vowel in the word is [+ATR], all other

vowels in the same word would be expected to surface as [+ATR], as in (2e).

However, in (2a) through (2d), the medial vowel [a] does not agree with the

word-final vowel in [ATR] specification, and the mid vowels in the first syllable

of the word agree with the medial vowel [a] in [ATR] specification. As a result,

the medial vowel [a] in these forms blocks the agreement or the spreading of the

[ATR] specification from the final vowel in these forms. Therefore, as the data in

(2) show, in Pulaar, the low vowel behaves opaquely and blocks the agreement or

the spreading of the [ATR] specification from the trigger.

The third pattern, which is represented in (c) in Figure 1 above, contains a

transparent or neutral vowel. In the transparent system, the medial vowel

(labeled as V2) does not agree with the trigger and the target; it does not

participate in harmony. The crucial difference between opacity and transparency

is that the final vowel, V3, agrees with the trigger vowel, and it has the same

feature specification as the trigger vowel. Finnish is often cited as an example of

transparency. In (3a) and in (3b), the data exhibit the total harmony pattern

where all the vowels in the word are identical in backness specification.

However, this generalization does not hold true in the forms in (3c) and (3d).

(3) Finnish Transparency and Neutral Vowel (Ringen and Heina‹ma‹ki 1999: 305 ) Root Suffixed Form Gloss

a. tØytæ tØytæ-næ ‘table/table-essive’

b. pouta pouta-na ‘fine weather/fine weather-essive’

c. koti koti-na (*koti-næ) ‘hand/hand-essive’

d) vero vero-lla (*vero-llæ) ‘tax-adessive’

In Finnish, the vowel in a suffix agrees in backness with the vowel(s) in the root.

For example, in (3a), the suffix vowel is [æ] because the vowels in the root are all

front ([-back]). Likewise, the suffix vowel in (3b) is [+back] since all the vowels in

the root are [+back].

However, this generalization does not hold true when the root contains a

neutral vowel, [i] or [e]. In (3c), the vowel in the suffix agrees with the vowel in

the first syllable even though the vowel in the second syllable, [i], is closer. Thus,

in this form, agreement/harmony skips over the medial neutral vowel, which

behaves transparently. (3d) shows that neutral vowels do not trigger harmony,

either; in (3d), there is a neutral vowel, [e], in the first syllable but the suffix

vowel agrees with the vowel in the second syllable. Thus, in Finnish, the neutral

vowels, [i] and [e], behave transparently if they are in a word-medial position. If

they are in the first syllable of a word, they do not trigger harmony.

Finally, the data in (4) illustrate the dominant-recessive case as observed in

Diola-Fogny. In this language, when a root is followed by a non-alternating

suffix /-ul/, which contains a [+ATR] vowel (that is, a dominant vowel), the root

vowel surfaces as [+ATR]. If, on the other hand, a non-alternating suffix is not

present in a word, the vowels in the root, which are underlyingly [-ATR], do not

surface as [+ATR] (recessive).2

(4) Diola-Fogny dominant-recessive harmony (Sapir 1965) (Square brackets indicate the root.) - The Alternation Patterns [-ATR] (non-ATR) ˆ ¨ ´ ø a

[(+)ATR] i u e o \

- Diola-Fogny [(+)ATR] Dominance Causative ([-en]/[-´n]) Toward the speaker ([-ul]) Gloss

a. [baj]-´n (*baj-en]) [b\j]-ul (*baj-¨l, *baj-ul) ‘have’

b. [jitum]-en (*[jitum]-´n) [jitum]-ul (*jitum-¨l, *jˆt¨m-¨l) ‘lead away’

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!2 The use of binary features ([+ATR] and [-ATR]) is solely for explanation

purposes; nothing hinges on these notations.

The causative suffix alternates depending on the ATR specification of the

vowel(s) in the root. In (4a), the causative suffix is realized as [-´n] because the

root vowel is [a], which is [-ATR] or non-ATR (so, all the vowels are recessive). In

(4b), on the other hand, the same suffix is realized as [-en] because of the ATR (or

[+ATR]) vowel(s) in the root.

The suffix [-ul] is non-alternating. Thus, the vowel in this suffix is always

[(+)ATR] regardless of the ATR specification of the vowel(s) in the root, and in

fact, this suffix triggers harmony on the vowel(s) in the root. In (4a), this

causative suffix changes the ATR specification of the vowel in the root, and as a

result, all the vowels in the word surface as [(+)ATR]. Thus, this is a case of

(+)ATR dominance. The pattern exhibited in (4b) is different from those in (a)

through (c) in Figure 1. In total harmony, opacity, and transparency, the trigger

of harmony is in a certain position, or more specifically, in a privileged position;

for example, in Yakut, the trigger of harmony is always in the first syllable, and

in Pulaar, the vowel in the last syllable always triggers harmony. However, in

Diola-Fogny, it is not the position in a word that determines the trigger. Rather,

the specification of a vowel determines the type of harmony. In the causative

form in (4a), there are no [(+)ATR] vowels in the word, and as a result, no vowel

causes (+)ATR harmony (the recessive case). In the ‘toward the speaker’ form,

on the other hand, there is a dominant [(+)ATR] vowel in the suffix, and this

[(+)ATR] vowel affects the ATR specification of the vowel in the root. As a result,

this form exhibits a dominant pattern, where all the vowels surface with a

dominant value.

According to Steriade (1995), the dominant value in ATR harmony is

language-specific. For example, Diola-Fogny and Kinande (Archangeli and

Pulleyblank 1994; Sasa 2004, 2006) are cited as cases of [+ATR] dominance while

Archangeli and Pulleyblank cite Yoruba and Javanese as examples of

[-ATR]/[RTR] dominance.

Several approaches have been proposed within Optimality Theory to

account for the vowel harmony patterns outlined above. In the next section, an

overview of these OT treatments of vowel harmony is presented and the

predictions of each account are discussed.

1.2 An Optimality-Theoretic Account of Vowel Harmony

In this section, three of the OT approaches that are commonly assumed in

the literature are introduced: namely, feature alignment, feature linking, and

local agreement. The main purpose of this section is to discuss the theoretical and

empirical problems or issues with these three traditional approaches. Some of

the more recent developments are introduced in Section 1.3 of this chapter.

1.2.1 Feature Alignment

One of the earliest OT approaches to harmony is feature alignment. Under

this approach, families of alignment constraints are assumed for features such as

[back] and [round], along with faithfulness constraints and markedness

constraints. For example, in Kirchner’s (1993) account of Turkish backness and

roundness harmony, the alignment constraints for backness and roundness are

assumed to account for the harmony patterns observed in this language.

The formulation of a feature alignment constraint is presented in (5).3

(5) Align [F], PrWd-R (cf: Kirchner 1993: 6) For any parsed feature [F] in morphological category MCat (=root, word), F is associated to the rightmost syllable in MCat (violations assessed in a scalar fashion).

The constraint in (5) is satisfied when every instance of a feature [F] in a domain

(such as ‘a word’) is associated with the rightmost vowel.

Along with harmony constraints (an example of which is the alignment

constraint in (5)), markedness constraints and the No Gap constraint (and the

ranking of these constraints) play a role in accounting for harmony phenomena.

The definition of No Gap is presented in (6).

(6) No Gap (Levergood 1984; Archangeli and Pulleyblank 1994; Ito, Mester, and Padgett 1995: 598; Ringen and Vago 1998: 410)

Gapped configurations are prohibited. A gapped configuration is presented in Figure 2.

*V1 V2 V3 [F] Figure 2. A Gapped Configuration !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3 Even though the actual constraint formulation or definition is different from

that of alignment constraints, No Intervening constraints (Ellison 1995, Ringen and Vago 1998) yield similar effects.

In the configuration presented in Figure 2, the feature [F] is associated with V1

and V3, skipping the medial vowel. No Gap prohibits skipping a medial segment.

The tableaux in (8) through (10) present harmony patterns predicted by

the alignment constraint approach. In addition to an alignment constraint, a

markedness constraint and the No Gap constraint are also assumed. In addition

to (5) and (6), let us assume a hypothetical markedness constraint in (7).

(7) V2!"[!F] V2 may not be specified as [!F]. The markedness constraint prohibits the medial vowel V2 from being specified as

[!F]. An example of such a markedness constraint is *! (no high back unrounded

vowel) or *æ (no low front [+ATR] vowel). For purposes of exposition, in the

following tableaux, the leftmost vowel, labeled as V1, is assumed to be the

trigger of the harmony, and it is specified as [! F]. In (8) and in the subsequent

tableaux, it is assumed that in a transparent candidate (as in (8c)), where no

feature is associated with V2, a default feature is assigned to this vowel in the

phonetics. In (8) and in the subsequent tableaux, for the sake of argument, let us

assume that the feature [!F] is not compatible with the medial vowel V2, but [!F]

is compatible with the two vowels V1 and V3.4

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4 That is, associating [!F] with V2 creates some marked segment, such as a [+low,

+ATR] vowel, which tends to be avoided cross-linguistically.

(8) Total harmony is predicted: Align-R, No Gap >> Markedness /V1 V2 V3/

Align-R No Gap V2!"[!F]

!a) V1 V2 V3

[!F] (Total)

b) V1 V2 V3

[!F] ["F] (Opaque)

c) V1 V2 V3

[!F] (Transparent)

The three candidates in (8) are not the only possible candidates from the same

input. An additional case with another possible candidate is discussed later in this

section.

In (8), candidate (8a), total harmony, is selected as optimal. Candidate (8b),

the opaque case, loses because of the feature alignment constraint; in this

candidate, the feature [!F], which is associated with the initial vowel, misses the

right edge of the word by two vowels. Candidate (8c), the transparent candidate,

satisfies the alignment constraint, but this candidate violates the No Gap

constraint. Thus, as (8) shows, a feature alignment constraint accounts for total

harmony when both the alignment constraint and the No Gap constraint

dominate a markedness constraint.

(9) shows that an alignment constraint is also capable of accounting for an

opaque harmony system:

(9) Opacity is predicted by the ranking Markedness, No Gap >> Align-R /V1 V2 V3/

V2!"[!F] No Gap Align-R

a) V1 V2 V3

!b) V1 V2 V3

[!F] ["F]

c) V1 V2 V3

In (9), the high-ranked markedness constraint excludes the total harmony

candidate (9a); in this candidate, the medial vowel is specified as [!F], but the

markedness constraint militates against such a configuration. Candidate (9c)

loses because of No Gap, and as a result, candidate (9b), the opaque candidate, is

selected as optimal.

Feature alignment also accounts for a transparency case, as in (10). In (10),

with No Gap low-ranked, the transparent candidate is selected.

(10) Transparency is predicted by the ranking Align-R, Markedness >> No Gap /V1 V2 V3/

Align-R V2!"[!F] No Gap

a) V1 V2 V3

b) V1 V2 V3

[!F] ["F]

!c) V1 V2 V3

(10c) satisfies both the alignment constraint and the markedness constraint, while

(10a) violates the markedness constraint and (10b) incurs two violations of the

alignment constraint.

As seen in (8) through (10), the alignment approach accounts for all three

attested harmony cases. However, as pointed out in McCarthy (2002), there are

two issues with regard to the alignment approach to harmony; first, alignment

constraints can be satisfied in multiple ways, and as a result, the analysis with

alignment predicts unattested harmony patterns. Second, the analysis with

alignment mischaracterizes harmony processes in general. These two points are

illustrated in the tableau in (11), where candidate (11b), along with (11a), satisfies

Align [F], PrWd-R.

(11) Unattested pattern is predicted with Align-R, No Gap >> Markedness /V1 V2 V3/

a) V1 V2 V3

!b) V1 V2 V3

Align [F], PrWd-R is satisfied as long as the final vowel (in (11), the vowel labeled

as V3) is specified as [!F]. The two candidates in (11) satisfy both the No Gap

constraint (since a gapped configuration is not observed in either one of the two

candidates) and the markedness constraint (since the medial vowel is not

specified as [!F]). As a result, in (11), the markedness constraint (that prohibits

V2 from being specified as [!F]) prefers candidate (11b) to (11a).

(11) illustrates two problems with regard to the alignment analysis of

harmony. First, since there are multiple possible ways to satisfy an alignment

constraint, an unattested form, such as candidate (11b), can be selected as

optimal. Second, the fact that (11b) wins (in which the feature [!F] moves to the

(right) edge) shows that vowel harmony is characterized as a phenomenon in

which a certain feature reaches to either the right or the left edge of a word,

without necessarily being realized in any of the other vowels in the word. Such a

characterization is, needless to say, incorrect.

In (11), candidate (11b), in which the feature [!F] moves to the right edge,

is selected as optimal, but such a case is not attested in any harmony languages.

That is, if V1 is specified as [!F] but the following vowel V2 may not be specified

as [!F], then the result is either i) only V1 is specified as [!F] but V2 blocks the

spreading of [!F] to V3, or ii) [!F], which is associated with V1 is linked to V3

while skipping V2 (that is, transparency). However, alignment constraints are

satisfied as long as the feature which is targeted by the alignment constraint is

aligned with the specified edge (in (11), the right edge of the word); the

alignment constraint alone fails to block such an unattested pattern.

It is not impossible, however, to resolve the problem described above.

McCarthy (2002: 25) suggests, for example, the use of the Anchor constraint (in

this particular case, Anchor-Left, which requires that the feature associated with

the leftmost vowel in the input is present on the leftmost vowel in the output).

Another possible way to rule out a candidate as in (11b) is to assume an Input-

Output faithfulness constraint as in (12). The faithfulness constraint in (12) is a

positional faithfulness constraint that maintains the input-output identity of the

vowel in the first syllable (that is, the vowel labeled as V1).

(12) Ident I-O [!F] (#1) (cf. Beckman 1997, 1998; Sasa 2001) Segments in the first syllable of a word in the output have the same specification as their input correspondents for the feature [!F].

The analysis with (12) is presented in the tableau in (13).

(13) Total Harmony Predicted: Faith, Align-R, No Gap >> Markedness /V1 V2 V3/

Ident I-O [!F] (#1)

!a) V1 V2 V3

b) V1 V2 V3

In (13), both (13a) and (13b) satisfy the alignment constraint. However, candidate

(13b) is excluded by the positional faithfulness constraint; in (13b), the input

vowel V1 is specified as [!F] but its output correspondent is not identical to its

input correspondent in [!F]. The same effect would be obtained by assuming an

anchoring constraint in (13) since the feature [!F] associated with the initial

vowel in the input is not anchored to the leftmost vowel in the output.5

It is true that the problem in (11) can be resolved by assuming a positional

faithfulness constraint, as in (12), or by assuming an anchoring constraint as

suggested by McCarthy. However, the problem in (11) is, in fact, a more

fundamental one; the alignment approach mischaracterizes the harmony

process. As seen in (11), alignment constraints are satisfied as long as the feature

that an alignment constraint targets/refers to is associated with the vowel either

at the right edge (that is, in the word-final position, or in the word-final syllable)

or at the left edge. This implies that the analysis with alignment characterizes

harmony as a phenomenon in which a certain feature aligns with the edge(s) of a

word, for example, by moving a feature, as seen in (11b). Such a characterization

is incorrect, since, as discussed earlier in this chapter, vowel harmony is a process

in which vowels in a certain domain agree with a certain vowel in a certain

feature. Hence, using alignment in accounting for vowel harmony is eliminated

for empirical and theoretical reasons; empirically, the alignment analysis fails to

block unattested harmony patterns. Theoretically, it provides a

mischaracterization of the harmony phenomena.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5 It should be noted, however, that this problem is not unique to the alignment

analysis; as will be discussed in Chapter 4, other approaches (feature spreading and ABC) require positional faithfulness constraint(s) to predict the attested harmony patterns.

In addition to these, there is one more issue to be mentioned with regard

to the alignment approach, namely, gradient assessment; consider a hypothetical

case in which the final vowel does not participate in harmony but harmony goes

as far as it can go. The analysis of such a hypothetical case is presented in (15). In

(15), along with the positional faithfulness constraint and the alignment

constraint, a different markedness constraint (14) that prohibits the final vowel

(labeled as V3) from being specified as [!F] is also included.

(14) V3!"[!F]

V3 may not be specified as [!F]. (15) Final vowel as a blocker: Markedness >> Align-R /V1 V2 V3/

Ident I-O [!F] (#1)

V3!"[!F] Align-R

a) V1 V2 V3

!b) V1 V2 V3

c) V1 V2 V3

In the hypothetical case presented in (15), the final vowel V3 does not participate

in harmony; this is captured by the markedness constraint (ranked above the

alignment constraint) prohibiting V3 from being specified as [!F]. In (15), the

alignment constraint prefers (15b) to (15c) because in (15b), the feature [!F]

misses the right edge by one vowel while in (15c), it misses the right edge by two

vowels. In other words, in (15), the alignment constraint evaluates the candidates

gradiently, in that it counts by how many vowels the feature misses the right edge.

McCarthy (2002, 2003), suggests, however, that all OT constraints are

categorical, meaning that they are either satisfied or violated. In other words,

McCarthy claims that there should be no gradient constraints that count the

number of violations.6 As stated, in (15), it is crucial to assess candidates

gradiently in enforcing (more) harmony. However, if categorical assessment of

the alignment constraint is assumed, the alignment constraint fails to favor the

candidate with more complete harmony. This is illustrated in (16).

(16) Categorical Align-R fails to favor more harmony /V1 V2 V3/

Ident I-O [!F] (#1)

V3!"[!F] Align-R

a) V1 V2 V3

b) V1 V2 V3

c) V1 V2 V3

In (16), both candidate (16b) and (16c) equally violate the alignment constraint if

a categorical assessment is assumed. In (16b), more vowels participate in a

harmony process triggered by V1 than in (16c). However, if categorical

assessment is employed, there is no way to distinguish the candidates in (16b)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!6 This problem is not apparent in the case where a feature can reach the edge of a

word, as in (8) through (10).

and (16c). It is true that the selection of the actual candidate depends on the

ranking of other constraints (such as markedness constraints), but (16) illustrates

that categorical alignment constraints fail to force more vowels to participate in a

harmony process.

McCarthy acknowledges that categorical assessment means that it is not

possible to employ alignment constraints to account for vowel harmony. In fact,

he further claims that in the case of (16), for example, candidate (16b) (with more

harmony) should be selected not because the feature [!F] is closer to the right

edge in (16b) than in (16c), but simply because more vowels participate in

harmony in (16b) than in (16c). In other words, a harmony constraint should

favor a candidate where more vowels participate in harmony rather than

evaluate candidates depending on how close to or far away a feature is from the

designated edge.

To summarize, as seen in (8) through (10), it is possible to account for the

attested vowel harmony patterns by employing a feature alignment constraint.

However, as argued, there are three problems with the alignment approach;

first, it requires categorical assessment; second, alignment constraints favor

unattested forms if used without other mechanism (such as positional

faithfulness, and finally, it mischaracterizes harmony processes.

1.2.2 Feature Linking with Spread

The second approach to vowel harmony is to assume multiple feature

linking/sharing with Spread as a harmony constraint. The original definition of

the spreading constraint as given by Padgett (1997) is presented in (17).

(17) Spread [!F] (Padgett 1997: 22) Every feature [!F] is linked to every segment (Spread (x): $x,y, x(y): x= feature, y=segment).

Spread requires (multiple) feature linking, and the spreading constraint is

satisfied only when the same feature is shared by all of the vowels in a particular

domain. The tableaux in (18) through (20) show how Spread accounts for the

three basic harmony types (total, opacity, and transparency). In (18) through

(20), the positional faithfulness constraint for the initial vowel, Ident I-O [!F] (#1)

in (12), is assumed to be undominated; any candidate/possible representation in

which the initial vowel is not faithful to its input correspondent is excluded by

this positional faithfulness constraint.

(18) Total harmony with the ranking Spread [F], No Gap >> Markedness /V1 V2 V3/

Spread [!F] No Gap V2!"[!F]

!a) V1 V2 V3

b) V1 V2 V3

[!F] ["F]

c) V1 V2 V3

(18) shows that total harmony is accounted for by the ranking Spread, No Gap

>> Markedness (V2!"[!F]). In (18), candidate (18a) completely satisfies Spread

[!F]; in this candidate, the feature [!F] is multiply linked to all of the vowels in

the word. Candidate (18c) incurs two violations of this spreading constraint; the

feature [!F], which is associated with V1, is not linked to two of the vowels, V2

and V3. Candidate (18b) violates the spreading constraint once for V2, with which

the feature [!F] is not associated. Tableau (18) is analogous to the tableau in (8),

where an alignment constraint is assumed, in that as long as the harmony

constraint (Align-R in (8) and Spread [F] in (18)) along with No Gap dominates

the relevant constraint, total harmony is accounted for.

(19) is the analysis of opacity with Spread. (19) shows that as long as a

markedness constraint and the No Gap constraint dominate the harmony

constraint, as in (10), an opacity candidate is selected as optimal when Spread is

employed as a harmony constraint.

(19) Opacity is predicted by the ranking Markedness, No Gap >> Spread /V1 V2 V3/

V2!"[!F] No Gap Spread [!F]

a) V1 V2 V3

!b) V1 V2 V3

[!F] ["F]

c) V1 V2 V3

As in (9), the markedness constraint prohibits the feature [!F] from being

associated with V2. Because of this markedness constraint, candidate (19a) is

excluded from the competition. (19c) loses because of No Gap even though this

candidate performs better than (19b) under Spread; in (19c), [!F] skips only one

vowel while in (19b), [!F] is not linked to two of the vowels. Thus, as seen in

(19), an opacity pattern is accounted for by Spread as long as this constraint,

along with No Gap, dominates a markedness constraint.

Thus far, both the alignment analysis and the spread analysis make the

same predication; the same ranking accounts for total harmony and an opacity

case in the alignment analysis and in the spreading analysis. In the transparency

case, on the other hand, there is a small difference between these two

approaches. This is illustrated in (20).

(20) Transparency predicted by the ranking Markedness >> Spread >> No Gap /V1 V2 V3/

V2!"[!F] Spread [!F] No Gap

a) V1 V2 V3

b) V1 V2 V3

[!F] ["F]

!c) V1 V2 V3

(10) in Section 1.2.1 showed that the transparency case is accounted for by the

alignment constraint if the alignment constraint and a markedness constraint

both dominate the No Gap constraint. In accounting for transparency with a

feature alignment constraint, it is not necessary to establish a ranking between

the alignment constraint and the markedness constraint.

(20) shows, on the other hand, that it is necessary to establish the ranking

Markedness (V2!"[!F]) >> Spread if a spreading constraint is assumed to account

for transparency. The difference between the analyses in (10) and (20) lies in the

difference in the assessment by an alignment constraint and a spreading

constraint; a transparency candidate does not violate the feature alignment

constraint (and thus, total harmony and a transparent candidate tie under the

alignment constraint) while as seen in (20), the transparency candidate does

violate Spread. Thus, it is necessary to exclude a total harmony candidate from

the competition before the spreading constraint assesses violations in the

(remaining) candidates.

As seen in (18) through (20), the analysis with Spread makes the same

predictions as the analysis with a feature alignment constraint. The same ranking

accounts for total harmony and opaque harmony under both an alignment

approach and a spreading approach. The analysis with Spread is also capable of

predicting transparent harmony. One small difference between the alignment

analysis and the feature linking analysis is that unlike in an alignment analysis, a

fixed ranking is necessary between a markedness constraint and a spreading

constraint, if Spread is employed as a harmony constraint.

1.2.3 Local Agree

The third type of harmony constraint that has been widely assumed is

Agree. The definition of an agreement constraint is presented in (21).

(21) Agree [!F] (cf. Bakovic 2000) Adjacent segments (vowels) agree in the feature [!F]. Two things need to be pointed out as differences between Agree and

other harmony constraints, such as Align or Spread. First, with the agreement

constraint, the domain of evaluation is local and the agreement constraint

performs a pair-wise comparison of adjacent vowels. Figure 3 presents the

evaluation by Agree for the three basic harmony patterns (total, opacity, and

transparency):

/V1 V2 V3/

a) V1 V2 V3

[! F] [! F] [! F] (total)!

b) V1 V2 V3

[! F] [" F] [" F] (opaque)!

c) V1 V2 V3

[! F] [" F] [! F] (transparent)!

Figure 3. Evaluation under Agree 1 In Figure 3, candidate (a), the total harmony pattern, fully satisfies the agreement

constraint: in both vowel pairs, V1-V2"and V2-V3, two adjacent vowels are

specified as [!F]. Candidate (b) violates this constraint once: the pair of vowels

V2-V3 is specified as ["F], but in the other pair, V1-V2, the two vowels are not

specified in the same way in terms of the feature [F]. Thus, Agree assigns a

violation to this V1-V2 pair. (23c), the transparent candidate, violates this

agreement constraint twice: one violation for the V1-V2 pair, and the other

violation for the V2-V3 pair. Thus, as seen in Figure 3, Agree performs a pair-wise

comparison and assigns a violation for a pair that does not agree (or in which the

two vowels do not have the same specification) with regard to the feature [!F].

The other difference between Agree and Spread is that the agreement

constraints are satisfied whether or not the same feature is associated with two

adjacent vowels. That means that the following two configurations in Figure 4 tie

under the agreement constraint.

/V1 V2/

Agree [!F]

a) V1 V2

b) V1 V2

[!F] [!F]

Figure 4. Evaluation under Agree 2 In Figure 4, the phonetic realization of the two candidates is the same. The only

difference between these two candidates in Figure 4 is that in (a), the same

feature [!F] is shared by two vowels while in (b), these vowels each have a

different feature [!F]. Therefore, in the evaluation under the agreement

constraint, it does not make a difference whether the same feature is shared or

not. Note that the configuration in (b) violates Spread [!F] (“Every feature [!F]

is linked to every segment”) twice, while both (a) and (b) satisfy the feature

alignment constraint.

The tableaux in (22) and (23) present the analysis with Agree. As before,

Markedness (V2!"[!F]) prohibits V2 from being specified as [!F]. Since multiple

feature linking is not required for Agree, the constraint No Gap is not included in

the following tableaux; in (22) and (23), total harmony and opacity are predicted,

but transparency cannot be predicted by the ranking permutations of the two

constraints, Agree and Markedness.

(22) Agree >> Markedness prefers total harmony /V1 V2 V3/

Agree V2!"[!F]

! a) V1 V2 V3

[! F] [! F] [! F] (total)

b) V1 V2 V3

[! F] [" F] [" F] (opaque)!

c) V1 V2 V3

[! F] [" F] [! F](transparent)!

(22) shows that when the ranking Agree >> Markedness (V2!"[!F]) is established,

total harmony is predicted; (22a) totally satisfies the agreement constraint while

(22b) violates this constraint once (for the V1-V2 pair) and (22c) incurs two

violations. Thus, Agree is capable of accounting for total harmony as seen in (22).

When the ranking between the agreement constraint and the markedness

constraint is reversed, as in (23), an opaque candidate is predicted:

(23) Markedness >> Agree prefers opacity /V1 V2 V3/

V2!"[!F] Agree

a) V1 V2 V3

[! F] [! F] [! F] (total)

! b) V1 V2 V3

[! F] [" F] [" F] (opaque)!

c)V1 V2 V3

[! F] [" F] [! F] (transparent)

In (23), candidate (23a) is excluded from the competition because of the

markedness constraint. Between the remaining candidates, (23b) and (23c), (23b),

the opaque candidate, performs better than the transparent candidate under the

agreement constraint. Thus, as seen in (23), when the ranking Markedness (V2!"

[!F]) >> Agree is established, it is possible to predict an opaque pattern

employing the Agree constraint.

However, the analysis in (22) and (23) presents a problem; if Agree is

employed as a harmony constraint, it is not possible to select a transparency

candidate as optimal. (23) shows that when an agreement constraint is higher-

ranked than the markedness constraint, then total harmony is predicted. In (22),

the opacity pattern is selected as optimal when the markedness constraint

dominates the agreement constraint. However, neither one of the ranking

permutations predicts a transparency pattern. This problem has been addressed

by Bakovic and Wilson (2000, 2004); as they point out, an opacity harmony

pattern always performs better than a transparency pattern with regard to

Agree. In other words, if Agree is employed as a harmony constraint, then it

always prefers an opaque candidate to a transparency candidate. To resolve this

problem, Bakovic and Wilson propose an additional OT mechanism referred to

as a targeted constraint.

However, there are some theoretical and empirical critiques with regard

to targeted constraints. First, Finley (2008) points out that the version of targeted

constraints that is presented in Bakovic and Wilson (2004) fails to predict the

transparency patterns (even though their original proposal of targeted constraint

successfully accounts for the transparency in Wolof). McCarthy (2008) also points

out that the case of cluster simplification (which requires targeted constraints,

according to Bakovic and Wilson (2004)) can be explained by other alternatives

(deletion as attrition; see Chapter 6). Finally, Rubach (2004) casts strong doubt as

to the existence of targeted constraints as part of the OT grammar, and claims

that the analysis with targeted constraints (as proposed by Burzio (2001)) makes

an incorrect prediction in accounting for the diphthongization phenomena

observed in Slovak. These considerations lead us to ask one question: is the

agreement approach viable, given these critiques with regard to targeted

constraints, which the analysis with Agree crucially relies on? In other words, the

analysis with Agree would be proven to be empirically inadequate if the

existence of targeted constraints were to be denied in the OT grammar.

As seen in (22) and (23), Agree is capable of predicting or accounting for

total harmony or an opaque harmony pattern. However, the analysis with local

Agree faces a challenge in accounting for transparency since, as seen in (23),

Agree always prefers opacity to transparency if it is employed without any

additional mechanism, such as targeted constraints that prefers transparency to

opacity. Thus, it is not empirically possible to predict a pattern where a medial

vowel behaves transparently in harmony if Agree with no additional

mechanisms is employed as a harmony constraint.

1.2.4 Summary

The predictions made by the three approaches discussed thus far are

summarized in Table 1. Table 1 shows that all three approaches, alignment,

spread, and agreement, are capable of accounting for total harmony. When a

harmony constraint dominates a markedness constraint, total harmony is always

predicted no matter which harmony constraint is employed. The opacity pattern

can also be accounted for by all three approaches, as long as the ranking No Gap

>> Harmony is established.

Table 1. Predictions under Align, Spread, and Agree Total

Harmony Opaque Transparent Notes

Align " Predicted (with No Gap being high-ranked)

" Predicted (with Markedness and No Gap dominating Align)

" Predicted (with No Gap being low-ranked)

It is crucial to assume gradient violation to enforce harmony

Spread " Predicted " Predicted (with Markedness and No Gap dominating Align)

" Predicted (necessary to establish the ranking, Markedness >> Spread)

Multiple feature linking is necessary

Agree " Predicted " Predicted !!not predicted (Agree always prefers opaque)!

The transparency case presents an interesting difference among these

three approaches; first, the analysis with Agree fails to predict such a pattern, as

seen in the previous section. The transparency case is accounted for by both

Alignment and Spread as long as both a harmony constraint and a markedness

constraint dominate No Gap. There are several possible rankings to achieve

transparency with Alignment, while there is one possible ranking (Markedness

>> Spread), by which transparency is predicted with Spread as a harmony

constraint. Nonetheless, Spread is still capable of predicting or accounting for a

transparency pattern.

The tableaux in (22) and (23) show that the analysis with Agree is not

capable of predicting a transparent pattern; (22) and (23) show that no matter

what the ranking permutation of the agreement constraint and the markedness

constraint is, a transparent candidate is not the winner of the competition; when

the agreement constraint dominates the markedness constraint, total harmony is

preferred to opacity and transparency. When the ranking is reversed (and the

markedness constraint dominates the agreement constraint), then an opacity

candidate is selected as optimal. Therefore, an analysis with Agree encounters

difficulties when transparency is observed in harmony pattern.

1.3 Recent Developments: An Overview

In addition to the approaches presented in the previous section, several

novel approaches have been proposed to account for (vowel) harmony. Among

them are the Span Theory of harmony (McCarthy 2004, Smolensky and

Legendre 2006) and Agreement-By-Correspondence (ABC) (Rose and Walker

2004, Walker 2009). An overview of these two recent developments is presented

in this section.

1.3.1 Span Theory

One of the main assumptions in Span Theory is that segments in a word,

or in a harmony domain, are exhaustively parsed into (a) span(s). According to

McCarthy (2004: 4), a span is defined as “a constituent whose terminal nodes are

segments in a contiguous string.” Both McCarthy and Smolensky and Legendre

claim that each span contains a head, with the head determining the actual

pronunciation of the segments in a given span. McCarthy (2004) summarizes the

properties of a span as follows. First, there is only one head in a single span.

Second, parsing of segments into spans must be exhaustive; in other words,

every segment in the domain must be parsed into some span. In OT terms, GEN

does not create a candidate where non-exhaustive parsing of segments is

observed. Third, no overlapping spans are allowed. McCarthy suggests that the

first two properties resemble the association conventions of early autosegmental

phonology. For instance, the second property resembles the assumption that

“every tone bearing unit is associated with some tone (Clements and Ford 1979,

Goldsmith 1976),” and the third resembles the prohibition on crossing of

association lines.

McCarthy cites the example of nasal harmony (nasal spreading) in Johore

Malay to illustrate how the proposals are implemented in actual data. In Johore

Malay, if there is a nasal segment in a word, the nasality spreads to the following

segments (rightward from a [+nasal] segment). Vowels, glides, and liquids can

be nasalized but fricatives cannot be nasalized; they block the spreading of the

[+nasal] feature. Thus, for example, an input /mawasa/ surfaces as [ma~w~a~sa], in

which the fricative, [s], blocks the spreading of nasality to the following vowel.

To implement the theory, McCarthy suggests the following four types of

Span-Theoretic constraints. First, McCarthy proposes an anti-adjacent span

constraint that enforces harmony. An example of such a constraint is presented

in (24).

(24) *A-Span [Nasal] (McCarthy 2004: 7) Assign one violation mark for every pair of adjacent spans of the feature [nasal].

(24) favors a candidate in which all the segments are parsed into a single [+nasal

or [-nasal] span. If a segment is parsed into a [+nasal] span, it is realized as

[+nasal]. Likewise, if a segment is parsed into a [-nasal] span, then that segment

is realized as [-nasal]. (24) is analogous to Spread in the previous accounts, in that

it requires that all segments are exhaustively parsed into a single span.

Second, there are constraints that determine which segments block

spreading.

(25) Head([+Cont, -Son], [-Nasal])(McCarthy 2004: 7) Every fricative ([+continuant, -sonorant] segment) heads a [-nasal] span. The constraint in (25) requires that if there is a fricative in the output, it is the

head of a [-nasal] span. (25) is violated, for example, if a fricative is parsed into a

[+nasal] span. In this thesis, a constraint of the type illustrated in (25) is referred

to as a headedness constraint (a constraint that designates a head segment in the

output).7

The third Span-Theoretic type of constraint, as given in (26), is an input-

output faithfulness constraint whose function is twofold; for example, (26) states

that if there is a [+nasal] segment in the input, first, its output correspondent is

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7 One might ask whether it is possible to account for blocking effects by

assuming a markedness constraint (in this case, *s~ (“No nasalized fricatives”) instead of (25). As illustrated in (28) of this section, the headedness constraint in (25) is independently necessary to express the blocking effect.

specified as [+nasal], and second, its output correspondent is the head of a

[+nasal] span.

(26) FaithHeadSpan[Nasal] (FthHdSp[nasal]) (adapted from McCarthy 2004: 5) If an input segment %I is [+nasal] and it has an output correspondent %0, then %0 is the head of an [+nasal] span.

Under Span Theory, the constraint in (26) is one example of the only type of

faithfulness constraint, in that this constraint evaluates the faithfulness between

the input segment and its output correspondent. All other types of constraints in

Span Theory are markedness constraints, and they are all output-oriented.

According to McCarthy (2004: 5), (26) is violated in either one of these two

instances: when an input [+nasal] segment has an output correspondent but it is

the head of an oral span, or when an input [+nasal] segment has an output

correspondent that is not the head of any span of the feature [nasal]. This

suggests that (26) is silent with respect to a candidate in which the input [+nasal]

segment is deleted in the output.

Finally, there are constraints that determine the position of the head,

which are referred to as directionality constraints in this thesis.

(27) SpanHeadLeft[Nasal] (cf. McCarthy 2004: 12) The head segment of a [+nasal] or [-nasal] span is initial in that span. Assign one violation mark for each non-conforming span.

The constraint in (27) designates the location of a head in a given span. According

to McCarthy, constraints as in (27) determine the directionality of feature

spreading.

(28) is a Span-Theoretic account of Johore Malay nasal harmony using the

constraints in (24) through (27). In (28) (and in tableaux where a Span-Theoretic

analysis is presented), I follow McCarthy’s conventions; parentheses indicate a

span, and underlining indicates the head segment in a span.

(28) Span-Theoretic Analysis: /mawasa/_[ma~w~a~sa] /mawasa/ SpanHeadLeft

[Nasal] FthHdSp

[nasal] Head([+Cont, -Son], [-Nasal])

*A-Span [Nasal]

!a) (mawa)(sa) * b) (mawasa) *! c) (m)(awasa) *! * d) (bawasa) *(!) *(!) e) (maw)(asa) *! * In (28), candidate (28b) ([ma~w~a~s~a~]) loses because of the headedness constraint for

fricatives; in this candidate, the fricative undergoes nasalization and fails to

function as the head of a [-nasal] span. (28c), the pronunciation of which is

[mawasa], fails because of the directionality constraint since the head of the

[-nasal] span (the second span) is not initial. (28d) loses because of the faithfulness

constraint; in (28), the input contains a [+nasal] segment and its output

correspondent should be the head of a [+nasal] span. However, in (28d), the

output correspondent of the input nasal is not [+nasal] and does not head a [-

nasal] span. Finally, candidate (28e) loses because of Head ([+cont, -son],

[-nasal]); as in (28b), the fricative [s] in this candidate does not head a [-nasal]

span. Notice that a markedness constraint, *s~, which prohibits nasalizaed

fricatives, can exclude candidate (28b) (in which the fricative is nasalized), but the

markedness constraint fails to exclude candidate (28e) (in which the fricative

surfaces as [-nasal]). Thus, (28) shows that the headedness constraint is

independently motivated to achieve the blocking effect.

In (28), the ranking Head ([+cont, -son], [-nasal]) >> *A-Span [nasal]

crucially needs to be established. According to McCarthy, the ranking between

the headedness constraint and the anti-adjacent span constraint predicts the

blocking effect; in Johore Malay, the headedness constraint for fricatives

(requiring that a fricative head a [-nasal] span) dominates the anti-adjacent span

constraint, and this ranking captures the blocking effect, where a fricative blocks

the spreading of nasality.

As mentioned, Span Theory was originally proposed to account for

consonant (nasal) harmony. However, the theory has been extended to vowel

harmony, and several Span-Theoretic accounts have been proposed; these

include O’Keefe’s (2005) analysis of Wolof ATR harmony and Sasa’s (2007) and

Kenstowicz’s (2008) analyses of Kinande ATR harmony. A detailed presentation

and discussion of the application of Span Theory to vowel harmony is given in

Chapters 2 and 3 in this thesis.

1.3.2 Agreement By Correspondence (ABC)

Another major recent development in the OT treatment of harmony is

Agreement-By-Correspondence (ABC) as proposed by Rose and Walker (2004).

The essence of this approach is summarized as a ‘similarity-driven’ account of

harmony; the key claim is that output segments that are similar, or more

specifically, output segments that are identical for (a) certain feature(s), stand in

an output correspondence relation. In other words, a kind of output-output

correspondence, along with input-output correspondence and other kinds of

output-output correspondence, such as Base-Reduplicant (B-R) correspondence

(McCarthy and Prince 1995) or trans-derivational correspondence (Benua 1997),

is assumed to hold among output segments. A schematic representation of the

ABC-type correspondence is presented in Figure 5.

(input) /C V C/ !!!"!! !!!!!!!!!!!!!![!F]

" " " # I-O Correspondence (output) [Cx V Cx]

!!"! ! !! ! !!!!"! !! !!!!!!!!!!!![!F] [!F]

$Corr C-C correspondence% Figure 5. Correspondence in ABC Source: Rose, Sharon and Rachel Walker (2004). A typology of consonant agreement as correspondence. Language 80. 475-531. In Figure 5, C stands for a consonant and V stands for a vowel. In ABC,

subscripts, as in Cx or Cy, are used to indicate that segments are in output

correspondence. As seen in Figure 5, the ABC-type output-output

correspondence is more similar to B-R correspondence (McCarthy and Prince

1995), rather than to trans-formational/-derivational output-output

correspondence (Benua 1997); ABC correspondence evaluates the identity of

segments in a single output string, rather than evaluating identity between the

base of a paradigm and other forms that belong to the same paradigm (as is

proposed in Benua 1997).

Whether similar segments are in correspondence depends on the ranking

of the output correspondence constraint. The constraint in (29) requires that

consonants in the output that are similar in [!F] are in correspondence.

(29) Corr C[!F]-C[!F] (cf. Rose and Walker 2004: 491) Let S be an output string of segments and let Ci and Cj be segments that share a specified feature [!F]. If Ci and Cj belong to S, then Ci is in a relation with Cj; that is Ci and Cj are in correspondence with one another.

The ABC approach was originally proposed for consonant harmony, but

Walker (2009) presents an application of the proposal to vowel harmony. For

example, Walker (2009) proposes that the opacity and transparency observed in

Menominee ATR harmony are accounted for through ABC by blocking by

correspondence (BBC) and by lack of correspondence (TLC: Transparency by

Lack of Correspondence), respectively.

To implement the theory in the treatment of vowel harmony, Walker

(2009) proposes the following ABC constraints.

(30) Corr V[-lo]-V[-lo] (Walker 2009) Let S be an output string of segments and let X and Y be [-consonantal,

-low] segments. If X and Y belong to S, then X and Y correspond. The role of (30) is to require that output segments that are specified as

[-consonantal, -low] (that is, high and mid vowels) be in correspondence. Any

candidate in which there are non-low vowels which are not in correspondence

violates (30) at least once. Both Rose and Walker (2004) and Walker (2009) claim

that the correspondence relationship is restricted to segments that are identical

for a certain feature or for a certain class of features.

In ABC, the fact that two (or more) segments are in correspondence does

not, by itself, guarantee that the segments in correspondence are identical in

other features, say, the feature [+ATR] or [-ATR]. The constraint in (31) requires

that segments in correspondence for a certain feature be identical for the feature

[+ATR].

(31) Ident VV [+ATR] (Id VV [+ATR]) (Walker 2009) Let X be a segment in the output and Y be a correspondent of X in the output. If X is [+ATR], then Y is [+ATR].

Walker (2009) points out, citing Hansson (2006, 2007), that the evaluation of

constraints such as (31) is local; that is, when there is a string of segments,

[...V1x...V2x...V3x...V4x...], the output identity constraint performs a pair-wise

comparison, as #V1,V2$, #V2,V3$, and #V3,V4$.

The preliminary ABC approach to harmony is presented in (32); for

illustration purposes, let us assume a hypothetical language where a [+ATR]

feature spreads from left to right from the initial vowel and a [-low] vowel

becomes [+ATR] when after a [+ATR] vowel.

(32) An ABC Approach: /i-´-ø/_[i-e-o] /i-´-ø/ Corr V[-lo]-V[lo] Id VV [+ATR] Id I-O [ATR]

!a) ix ex ox ** b) ix ´ ø *!* c) ix ´x ox *!* *

In (32), there are other possible candidates from the same input, such as *[ˆ-´-ø],

but I assume that there are several other mechanisms/constraints that preserve

the identity of the trigger (the initial vowel), such as the initial syllable

faithfulness constraint in (13) above.

(32b) loses because of the output correspondence constraint; there are two

[-low] vowels in this candidate that are not in correspondence with the initial

vowel. (32c) loses because of the Id VV [+ATR] constraint; this candidate incurs

two violations of this faithfulness constraint (one each for the [i-´] pair and for

the [´-o] pair). In each pair, two vowels in correspondence are not identical with

respect to the feature [+ATR] (that is, one vowel is specified as [+ATR] but the

other is not).

(32) shows that the ranking Corr V[-lo]-V[lo], Id VV [+ATR] >> Id I-O

[ATR] accounts for the ATR harmony in this hypothetical case. Walker (2009)

suggests that in order for harmony to take place, the following ranking needs to

be established.

Corr V-V Ident V-V Ident I-O Figure 6. ABC Ranking for Harmony Source: Walker, Rachel (2009). Similarity-sensitive blocking and transparency in Menominee. Paper presented at the 83rd Annual Meeting of the Linguistic Society of America. San Francisco.

The ranking in Figure 6 shows that both the output correspondence constraint

and the output identity constraint dominate the input-output faithfulness

constraint. This suggests that in order for harmony to take place, it is more

important that output segments be in correspondence and be identical in the

feature as specified by the output identity constraint than for each output

segment to be faithful to its input correspondent.

Walker (2009) shows that the ABC approach, even though originally

proposed to account for long-distance consonant harmony, is applicable to

vowel harmony. The ABC approach to vowel harmony is further investigated in

this thesis; the application of ABC to other harmony languages is presented in

Chapters 2 and 4.

1.4 The Organization of the Thesis

In this chapter, five approaches to vowel harmony which have been

proposed in the previous literature have been discussed. Two of the approaches,

feature alignment and local agreement, were eliminated as discussed in Section

1.2. Therefore, for the remainder of this thesis, three approaches, i) the feature

spreading analysis, ii) Span Theory, and iii) ABC (Agreement By

Correspondence) are further examined with the attested harmony data. In

Chapter 2, the application and the implementation of these three approaches are

presented with data from Turkish (Turkic). Chapter 3 and Chapter 4 both deal

with the case study of Pulaar ATR harmony; Chapter 3 concentrates on the Span-

Theoretic analysis of Pulaar ATR harmony and Chapter 4 is a comparison and

detailed discussion of the feature linking analysis and the ABC analysis with the

Pulaar ATR harmony data. In Chapter 5, backness and roundness harmony is

revisited but with data from a Yakut, another Turkic language.

CHAPTER II TURKISH VOWEL HARMONY: A CASE STUDY

In Chapter 1, I introduced five approaches that have been proposed to

account for vowel harmony in the OT framework. Among those five

approaches, the feature alignment approach can be eliminated for theoretical

reasons; it requires gradient assessment and, more crucially, it mischaracterizes

the phenomenon. The analysis with local agreement is empirically inadequate in

that such an approach requires some additional mechanisms to fully account for

the attested vowel harmony patterns. For the remainder of this thesis, the

remaining three approaches, i) feature linking, ii) the Span Theory of harmony,

and iii) Agreement by Correspondence (ABC), are discussed and examined with

attested vowel harmony data.

The main purpose of this chapter is to present a case study of Turkish

vowel harmony to show that these three approaches successfully account for the

attested harmony patterns in Turkish. It is demonstrated that even though ABC

and Span Theory were originally proposed to account for consonant harmony,

they are able to account for vowel harmony data.

2.1 Turkish Vowel Harmony

! The vowel inventory of Turkish is presented in Table 2. The Turkish

vowel inventory is completely symmetrical; all the front vowels have a [+back]

counterpart and all the unrounded vowels have a [round] counterpart.

Table 2. Turkish Vowel Inventory [-back] [+back] non-[round] [round] non-[round] [round] [+high] i y ! u [-high] e Ø a o Source: Kornfilt, Jaklin (1990). Turkish and the Turkic languages. In Bernard Comrie (ed.) The World’s Major Languages. New York: Oxford University Press. 619-644.

Turkish is known for its vowel harmony, exhibiting both backness

harmony and roundness harmony; the roundness and backness specifications of

the suffix vowel(s) depend on the vowel(s) in the root. The data in (1) illustrate

the basic backness/roundness harmony patterns.

(1) Turkish harmony (Lightner 1972: 348)

Root 1st sg. Possessive Plural Gloss

a. Økyz Økyz-ym Økyz-ler (*Økyz-lØr) ‘loaf’

b. somun somun-um somun-lar (*somun-lor) ‘ox’

In (1), the vowels in the suffixes agree with the root vowels in backness; in (1a),

the root vowels are both [-back] and the vowel in the suffix is also [-back].

Likewise, the suffix vowels in (1b) are both [+back] because the root vowels are

[+back]. Thus, in backness harmony, the backness specifications of the suffix

vowels are identical to that of the vowels in the root.

The roots in (1) are harmonic since all (both) of the vowels in the root are

identical in backness and roundness. In addition to the harmonic roots in (1),

there are disharmonic roots in Turkish, in which not all vowels agree in their

backness specification. Examples of disharmonic roots and the treatment of such

roots are discussed later in this chapter, in Section 2.5.

In roundness harmony, on the other hand, there is an asymmetry in the

occurrence of [+high] round vowels and [-high] round vowels. In the root, any

round vowels freely co-occur, as the roots in (1a) and (1b) show. In suffixes,

[+high] round vowels are observed when the root contains round vowels, as

seen in the 1st sg. possessive forms. The [-high, round] vowels, on the other

hand, are not observed in suffixes; for instance, in (1a), the vowel in the plural

suffix is [-e] even though it is preceded by round vowels in the root. The same is

observed in (1b); the suffix vowel in (1b) is [-lar] even though it is preceded by

[+high, round] vowels.

The data in (2) show that the suffix [-high] vowels are unrounded even if

they are preceded by [-high, round] vowels in the root.

(2) Turkish roundness harmony: additional data (Clements and Sezer 1982: 216)

Root Genitive Plural Gloss

a. kØj kØ-yn kØj-ler (*kØj-lØr) ‘village’

b. son son-un son-lar (*son-lor) ‘end’

Thus, (1) and (2) show that non-high round vowels are not observed in suffixes

in Turkish. High round vowels, on the other hand, are observed in suffixes when

the root contains a round vowel; as seen in (2a) and in (2b), the high vowel in the

suffix is round even when the root vowel is non-high.

Table 3 summarizes the restrictions on the occurrence of the non-high

round suffix vowels in Turkish.

Table 3. Restrictions on Roundness Harmony in Turkish Attested Unattested Front Vowels

- y-e - Ø-e

y-y (both [+hi])

Ø-y ([-hi]>[+hi])

*Ø-Ø (both [-hi])

*y-Ø ([+hi]>[-hi])

Back Vowels

- u-a - o-a

u-u (both [+hi])

o-u ([-hi]> [+hi])

*o-o (both [-hi])

*u-o ([+hi]>[-hi])

To summarize the data, first, the vowels in suffixes always agree with the root

vowel(s) in backness specification. In roundness harmony, on the other hand,

there are restrictions; high round vowels are observed in suffixes when the root

contains (a) round vowel(s). Non-high round vowels, on the other hand, may

not occur in suffixes, even when the root contains (a) round vowel(s).

The next three sections present the analysis of Turkish harmony; the

analysis with feature linking (Spread (Padgett 1997, 2002)) is presented in

Section2.2. In Section 2.3, the ABC analysis is presented, and the Span-Theoretic

analysis is presented in Section 2.4.

2.2 The Feature Linking Analysis

The analysis with feature linking is presented in this section. The following

two constraints are used to enforce two harmony processes in Turkish.

(3) Spread [back] (cf. Padgett 2002: 89) If a feature [+back] or [-back] is associated with a vowel, the same backness feature is linked to all of the vowels in a word.

(4) is the spreading constraint for roundness harmony; in the analysis, the

feature [round] is assumed to be privative.

(4) Spread [round] (cf. Padgett 2002: 89) If a feature [round] is associated with a vowel, the same roundness feature is linked to all of the vowels in a word.

As seen in Section 2.1, there are two harmony processes in Turkish; it is

necessary to assume two harmony constraints that enforce different types of

harmony.1 (3) is fully satisfied when a single [+back] or [-back] feature associated

with a vowel is shared by all the vowels in a word, Likewise, (4) is fully satisfied

when all the vowels in a word share the same [round] feature.

In Turkish, both backness and roundness harmony are root-controlled.

Thus, it is necessary to assume a mechanism that preserves the input-output

identity of the trigger in the root. The positional faithfulness constraint in (5)

preserves the input-output (I-O) identity of the trigger with respect to backness.

(5) Ident I-O [back] (Root) (Id (root) [back]) (cf. Beckman 1997, 1998) Segments in the root have the same specification as their input correspondents for the feature [back].

The positional faithfulness constraint in (6) is also necessary to preserve the I-O

identity of the trigger with respect to roundness.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"!Padgett (2002) presents a similar analysis of Turkish with Spread [color] (instead of assuming two separate spreading constraints), making different assumptions with regard to feature organization. The consequences of this different assumption by Padgett are discussed in detail in McCarthy (2003). See also Chapter 6 for a demonstration of Spread [color].!

(6) Ident I-O [round] (Root) (Id (root) [round]) (cf. Beckman 1997, 1998) Segments in the root have the same specification as their input correspondents for the feature [round].

I assume root faithfulness rather than initial syllable faithfulness (requiring that

the vowel in the first syllable of a word is identical to its input correspondent in

backness/roundness) because of disharmonic roots. Initial syllable faithfulness

predicts that there are no disharmonic roots, which is not the case in Turkish (An

analysis of Yakut backness /roundness harmony with initial syllable faithfulness

is presented in Chapter 5.)

In Turkish, non-high round vowels are not observed in suffixes. The

markedness constraint in (7) restricts the occurrence of [-high, round] vowels.

(7) *o/Ø (cf. Kaun 1995) Non-high [round] vowels are prohibited.

Finally, the following three general faithfulness constraints preserve the

input-output identity of the vowels.

(8) Ident I-O [high] (McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [high].

In Turkish, changing the vowel height is not attested as a means of achieving

(more) complete roundness harmony. The faithfulness constraint in (8), which

must dominate Spread [round], blocks such an unattested change, and preserves

the input-output identity of the height specification.

(9) Ident I-O [back] (Id [back]) (McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [back].

(10) Ident I-O [round] (Id [round]) (McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [round].

The analysis for total roundness harmony is presented in (11). The actual

output form is (11a), in which all of the vowels agree both in backness and

roundness; the suffix high vowel becomes round because of the preceding round

vowels in the root.

(11) Total harmony: /somun-im/_[somun-um] /somun-im/ Id (root)

[Round] Spread [back]

Spread [round]

Id [round]

Id [back]

!a) somun-um ! [round]

b) somun-im ! [round]

*(!)**

c) sam!n-!m *!* ** * d) somun-ym #! [round]

Both (11b) and (11d) incur three violations for Spread [back]; in these candidates,

the vowels in the root share the same backness feature [+back], but this feature

misses the vowel in the suffix (one violation). A [-back] feature is associated with

the suffix vowel, but this [-back] feature is not linked to the two vowels in the

root (two additional violations). In addition to Spread [back], (11b) also violates

Spread [round] since the [round] feature associated with the vowels in the root is

not linked to the vowel in the suffix. (In (11d), on the other hand, Spread [round]

is obeyed, since all the vowels share the same [round] specification.) (11c)

satisfies the spreading constraints for roundness and backness, but this candidate

fails because of the root faithfulness constraint. (11) shows the following two

ranking arguments; first, the two spreading constraints dominate the two

general faithfulness constraints for backness and roundness: Spread [round],

Spread [back] >> Ident [back], Ident [round]; second, Ident (root) [round]

dominates the markedness constraint (Ident (root) [round] >> *o/Ø).

The analysis for partial harmony is presented in (12). Since the suffix

contains a non-high vowel in (12), the suffix vowel surfaces as unrounded.

(12) Partial harmony I: non-high target does not participate in harmony /somun-ler/ Id (root)

[rd] Spread [back]

Spread [rd]

Id [back]

Id [rd]

! a) somun-lar !!!!!!!!!"$%&'()!

b) somun-lor !!!!!!!!*$%&'()!

c) sam!n-lar *!* * ** d) somun-ler [round]

In (12), candidate (12b) loses because of the markedness constraint for non-high

round vowels; all of the candidates in (12) except for (12c) violate this

markedness constraint due to the [o] in the root. However, (12b) incurs one

more violation of this constraint because of the non-high round vowel in the

suffix. (12c) satisfies both of the spreading constraints and the markedness

constraint, but this candidate is excluded by the root faithfulness constraint. (12d)

loses because of the spreading constraint, since this candidate is worse than the

actual form under either one of the spreading constraints. (12) shows three

ranking arguments. First the markedness constraint (*o/Ø) dominates the

spreading constraint: *o/Ø >> Spread [round]; second, the root faithfulness

constraint dominates the spreading constraint for roundness, Ident (root)

[round] >> Spread [round]; and finally, Ident [high] >> Spread [round].2

(13) shows that the rankings established in (11) and (12) account for the

data in which a root contains a non-high round vowel.

(13) Partial harmony II: non-high target does not participate in harmony /son-ler/ Id (root)

[round] Spread [back]

*o/Ø Spread [round]

Id [back]

Id [round]

! a) son-lar !!!!!!!!!"$%&'()!

b) son-lor !!!!!!!!*$%&'()!

c) san-lar *! * * d) son-ler [round]

Candidate (13b) loses because of the markedness constraint, and (13d) loses

because of the spreading constraint for backness. (13c) satisfies both of these

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!+!In (12), there is another possible candidate, *[somun-lur], in which a height change is observed in the suffix vowel. Even though this candidate satisfies Spread [round], it is excluded by the faithfulness constraint Ident [high] (that is, the ranking Ident [high] >> Spread [round] blocks such an unattested height change).

constraints, but this candidate is ruled out by the root faithfulness constraint. (13)

shows the ranking Ident (root) [round] >> *o/Ø.

Figure 7 presents the ranking summary of the spreading analysis of

Turkish harmony.

Ident I-O (root) [round] Spread [back] *0/Ø #!

Spread [round] Ident I-O [back] Ident I-O [round] Figure 7. Ranking Lattice: Turkish/Spread First, the ranking Spread [back], Spread [round] >> Ident I-O [round], Ident I-O

[back] guarantees that harmony takes place. As seen in (11), if the ranking of

these constraints is reversed, no harmony will be observed and the fully faithful

candidate will be selected as optimal.

Second, in Turkish, backness harmony is unrestricted; the vowel in the

suffix always agrees with the root vowel(s) in backness specification. This is

captured by the undominated constraint Spread [back]; that is, no markedness

constraints block the spreading of the backness feature, and as long as root

faithfulness is satisfied, the spreading constraint enforces backness harmony.

Roundness harmony, on the other hand, is restricted, and this restriction is

captured by the ranking *o/Ø >> Spread [round]. In other words, unlike

backness harmony, the spreading of the roundness feature is restricted so as not

to create any additional marked segments.

As seen in this section, an analysis with Spread successfully accounts for

the attested Turkish data. I demonstrated that the blocking of the spreading of

[round], that is, the ‘blocking effect,’ is captured by ranking the markedness

constraint above the spreading constraint. In the next section, the ABC analysis

of Turkish is presented; I demonstrate how ABC accounts for the blocking effect

observed in Turkish.

2.3 The ABC Analysis

The second approach to harmony to be examined in this section is

Agreement-By-Correspondence (ABC), as proposed by Rose and Walker (2004)

and Walker (2009). The theoretical assumptions of ABC are summarized in two

points. First, output segments that are similar in certain phonetic characteristic(s)

can be in correspondence. Second, there is an additional family of correspondent

faithfulness constraints, in addition to other standard OT faithfulness constraints

(such as a family of Ident I-O constraints), that requires that the segments in

correspondence be identical with respect to a feature [F].

The first assumption, that similar output segments can form a

correspondence relationship, is implemented in Turkish by the following ABC

constraint.

(14) Correspond V-V (Corr V-V) (cf. Rose and Walker 2004: 491) Let S be an output string of segments and let X and Y be [-consonantal]. If X and Y belong to S, then X and Y correspond.

(14) requires that segments that are similar, in that they are identical in the

feature [-consonantal] (that is, vowels), are in correspondence. (14) is violated

when a vowel is not in correspondence with other vowels in the output. In ABC,

whether segments in an output string are in correspondence depends on the

ranking of the correspond constraints, as in (14). In the analysis that follows, I

use subscripts (Vx...Vx) to show that vowels are in correspondence. (That is,

vowels with same subscript are in correspondence.)

In ABC, the mere fact that two or more vowels are in correspondence

does not guarantee that these vowels are identical in the feature [F]. There is

another ABC mechanism, more specifically, family of output correspondent

faithfulness constraints, that requires that the vowels (or segments) in

correspondence be identical in the feature [F]. The following two output identity

constraints require that vowels in correspondence are identical in backness and

roundness.

(15) Ident VV [round] (Id VV [round]) (cf. Rose and Walker 2004: 492, Walker 2009)

Let X be a segment in the output and Y be a correspondent of X. If X is [round], then Y is [round].

As stated, even if X and Y are in correspondence (and X and Y are vowels), this

alone does not guarantee that both X and Y are realized (or surface) with

identical [round] features. So, for example, if (15) dominates the input-output

faithfulness constraint, Ident [round], then it is predicted that harmony is

possible. If, on the other hand, (15) is dominated by the input-output faithfulness

constraint for roundness, then it is predicted that harmony will not take place.

(16) is another output correspondent faithfulness constraint requiring that

output correspondents be identical with respect to the feature [back].

(16) Ident VV [back] (Id VV [back]) (cf. Rose and Walker 2004: 492, Walker 2009) Let X be a segment in the output and Y be a correspondent of X. If X is [+back], then Y is [+back]. If X is [-back], then Y is [-back].

In addition to the ABC constraints listed in (14) through (16), the following

OT constraints, which were introduced in the spreading analysis above, are also

necessary for an ABC analysis; they are listed under (17), and they are repeated

from the previous section.

(17) a. Ident I-O [high] Correspondent input and output segments have the same specification for the feature [high].

b. Ident I-O [round] (root) (Id (root) [round])

Correspondent input and output segments in the root have the same specification for the feature [round].

c. Ident I-O [back] (root) (Id (root) [back])

Correspondent input and output segments in the root have the same specification for the feature [back].

d. Ident I-O [round] (Id [round])

Correspondent input and output segments have the same specification for the feature [round].

e. Ident I-O [back] (Id [back])

Correspondent input and output segments have the same specification for the feature [back].

f. *o/Ø Non-high [round] vowels are prohibited.

The ABC analysis for the total harmony is presented in (18).3

(18) Total harmony 1: Trigger and target both [+high] /somun-im/ Id (root)

[round] Corr V-V Id VV

[round] Id

[back]

!a) soxmuxn-uxm * * b) soxmuxn-im *! c) saxm!xn-!xm *!* ** * d) soxmuxn-!xm *!

In candidate (18a), all the vowels are in correspondence and thus, Corr V-

V is satisfied. All the vowels in (18c) are also in correspondence, but this

candidate loses because of the root faithfulness constraint. (18b) violates Corr V-

V because in this candidate, not all vowels are in correspondence. (18d) satisfies

the correspondence constraint, but this candidate is ruled out because of the

Ident VV [round] constraint; in (18d), not all the vowels in correspondence are

identical in the feature [round]. (18) shows that Corr V-V dominates the general

faithfulness constraint for [round] (Corr VV >> Ident I-O [round]), and the

correspondent identity constraint is ranked above the I-O faithfulness constraint

for the roundness feature (Ident VV [round] >> Ident [round]).

The analysis for partial harmony is presented in (19). In (19), I assume the

ranking Ident (root) [round] >> *o/Ø, as established in the spreading analysis; if

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!,!In (18), there is another possible candidate, *[soxmuxn-uxm], in which all the vowels are in correspondence but not all vowels are identical in backness. Such a candidate, however, is excluded by another output identity constraint, Ident VV [back], which is not included in (18) due to space limitations. !

the ranking of these two constraints is reversed, it is predicted that [-high, r0und]

vowels are not observed in the root, which is incorrect in Turkish. (This ranking

is established in (20) below.)

(19) Partial harmony I: Non-high vowel in the suffix /somun-ler/ Id(root)

[rd] Corr V-V

IdVV [Rd]

Id VV [back]

Id [round]

Id [back]

!a) soxmuxn-laxr * * * b) soxmuxn-loxr **! * * c) soxmuxn-ler *! * d) soxmuxn-lexr * * *!

In (19), all the candidates satisfy the Corr V-V constraint except for (19c),

in which the vowel in the suffix is not in correspondence with other vowels.

Among the remaining candidates, (19b) loses because of the markedness

constraint, and (19d) loses because of the output identity constraint for backness.

(19) shows that the markedness constraint dominates the output identity

constraint for roundness: *o/Ø >> Ident VV [round].4

Finally, (20) is the analysis of a case where there is a non-high round

vowel in the root; candidate (20c) satisfies the markedness constraint, but this

candidate violates the positional faithfulness constraint for the root. (20b) is

worse than (20a) with respect to the markedness constraint. Between the

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!-!In (19), there are more possible candidates from the same input; for example, such candidates as *[saxm!xn-laxr] or *[sexmixn-lexr]. These candidates satisfy all the output identity constraints and the markedness constraint. However, such candidates are excluded by the undominated positional faithfulness constraint for the root. Another logically possible candidate in (19) is *[soxmuxn-loxr], in which the suffix vowel changes to [+high]. However, the undominated height faithfulness constraint excludes such a candidate. !

remaining candidates, (20a), the actual form, and (20d), Ident VV [back] selects

the actual form. (20) shows that the root faithfulness constraint needs to

dominate the markedness constraint: Ident (root) [round] >> *o/Ø.

(20) Partial harmony III: Non-high vowel in the root /son-ler/ Id(root)

[rd] Corr V-V

IdVV [Rd]

Id VV [back]

Id [round]

Id [back]

!a) soxn-laxr * * * b) sox-loxr **! * * c) saxn-laxr *! * * d) soxn-lexr * * *! Figure 8 presents a summary of the analysis. Ident (root) [round] Corr V-V *o/Ø Ident VV [round], Ident VV [back] Ident I-O [round] Ident I-O [back] Figure 8. Ranking Lattice: Turkish/ABC The ranking lattice presented as Figure 8 shows the following two points; first,

the ranking in Turkish follows Walker’s (2009) claim that in order for harmony

to take place, the output identity constraint needs to dominate the input-output

identity constraint(s). As seen in Figure 8, the Turkish ranking Ident VV [round]

>> Ident I-O [round], for example, is analogous to Walker’s claim.

Second, the ranking *o/Ø >> Ident VV [round] is analogous to the ranking

from the analysis with Spread, that is, *o/Ø >> Spread [round]. In the last section,

I suggested that the constraint enforcing harmony needs to be dominated by the

markedness constraint to capture the blocking effect in Turkish. In ABC, the

output identity constraint enforces harmony, by requiring correspondent vowels

to be identical in a certain feature; as seen in (19), the output identity constraint is

dominated by the markedness constraint. Thus, the blocking effect is expressed

in a similar fashion in the spreading analysis and in the ABC analysis; it is

expressed by the ranking between the markedness constraint and the harmony

constraint. In both analyses, the markedness constraint and its ranking play a

role in expressing the blocking effect.

In the next section, the third approach to harmony, Span Theory, is

discussed. I demonstrate that Span Theory is also capable of handling the Turkish

data, and it employs a similar mechanism to explain the blocking effect.

2.4 The Span-Theoretic Analysis

The Span Theory of harmony was originally proposed by McCarthy

(2004) to account for the consonant (nasal) harmony in Johore Malay (Onn 1976),

where the harmony feature, [nasal], is binary. Sasa (2008) proposes the

application of Span Theory to vowel harmony, where some of the harmony

features are assumed to be privative, and suggests that some of the Span-

Theoretic mechanisms need to be revised so that the theory is applicable to

harmony with the assumption of privative features.

The organization of this section is as follows; in Section 2.4.1, the Span-

Theoretic mechanisms are introduced, and in the following section, the analysis

of Turkish roundness harmony is presented with the Span-Theoretic

mechanisms.

2.4.1 Span-Theoretic Constraints

As stated in Chapter 1, the original proposal of Span Theory is

characterized by the following two assumptions; first, all segments are

exhaustively parsed into spans. Second, each span contains a head which

determines the actual pronunciation of the segments in a given span. For

example, in nasal harmony in Johore Malay, nasality spreads to the right from a

[+nasal] segment, and vowels, glides, and liquids undergo nasal harmony.

However, fricatives do not participate in harmony; they block the spreading of

the [+nasal] feature. Thus, the input /mawasa/ surfaces as [ma~w~a~sa], where the

nasality from the initial nasal spreads to the following vowels and glide, but the

fricative [s] blocks spreading. In the Span-Theoretic representation, the actual

form is represented as [(mawa)(sa)]. Parentheses are used to indicate a span, and

underlining indicates a head segment. Thus, in the notation [(mawa)], [m],[a],[w],

and [a] are in a single span, and the underlined segment [m] is the head of this

In this example, [(mawa)(sa)], there are two spans that differ in nasality.

The first (left) span is a [+nasal] span since the [+nasal] sound, that is [m], is

designated as the head of the span, and all the segments in this span agree with

the head in the feature [+nasal]. Thus, the vowels and the glide in this span are all

realized as [+nasal], surfacing as [a~w~a~]. Likewise, in the second, or the right, span,

where the head of the span is designated as [s], the sounds in this span are

realized as [-nasal] (thus, [sa]). The original proposal of Span Theory requires

that all the segments are exhaustively parsed into (a) span(s), and all the

segments in a span share the same feature with the head, or agree with the head

for a certain feature (such as [$nasal]).

In order to enforce harmony, or more specifically, to force all the

segments in a certain domain into a single span, McCarthy (2004) proposes the

following Span-Theoretic constraint.

(21) !*A-Span [nasal] (McCarthy 2004: 7) Assign one violation mark for every pair of adjacent spans of the feature [nasal].

(21) is satisfied when all the segments in a harmony domain are exhaustively

parsed into a single [+nasal] or [-nasal] span. For example, [(mawasa)]

(=[ma~w~a~s~a~]) or [bawasa] (=[bawasa])) satisfies (21) while [(mawa)(sa)] incurs one

violation of (26) for the pair of adjacent spans observed in this representation.

If these proposals are applied in Turkish roundness harmony, the Span-

Theoretic representation of the form [somun-lar] is [(somun)(-lar)]. In this

representation, there are two spans, which differ in roundness; in the first, or the

left span, the head is the high [round] vowel [u] and another high vowel

following the head in the same span, [u], shares a [round] specification with the

head segment. The vowel in the suffix, that is, the vowel [a], is also parsed into a

span, since parsing of the segments is assumed to be exhaustive; GEN does not

create a candidate with a segment that is not parsed into a span.

However, if the feature [round] is assumed to be privative, two questions

arise; first, what motivates unrounded vowels (which lacks the feature [round])

to form a span? Second, what causes the violation of the constraint in (21) when

there are two spans that differ in roundness? To examine these two questions, let

us consider two candidates, [(somun-um)] and *[(somun)(-!m)]. In Turkish, the

occurrence of high [round] vowels in suffixes is unrestricted; the first form is the

attested form.

According to Steriade (1995: 148), “the absence [of a feature] cannot

spread and repeated absence does not violate the OCP...” In the unattested form,

*[(somun)(-!m)], it is clear that in the first (left) span, two vowels share the

feature [round]; they agree with each other in the feature [round]. However, in

the second (right) span, it is not clear what motivates the unrounded vowel to

form its own span because if privative [round] is assumed, unrounded vowels

are specified as ‘zero round,’ and as pointed out by Steriade, zero cannot spread

or be shared. Therefore, under the assumption of privative [round], it is not clear

how a span is assigned to unrounded vowels.

Second, even granting that unrounded vowels can form their own span,

the constraint in (21) fails to enforce harmony. In the competition between

[(somun-um)] and *[(somun)(-!m)], these candidates equally satisfy the

constraint in (21), since even in *[(somun)(-!m)], where the second span lacks the

[round] feature, there are no adjacent [round] spans.

Table 4. The Evaluation by the Original *A-Span [round] /somun-!m/ *A-Span [round]

a) (somun-um) (total harmony: attested) "

b) (somun)(-!m) (partial harmony: unattested) "

The form (a) in Table 4 satisfies the anti-adjacent span constraint for the feature

[round]; in this form, all the vowels are parsed into a single [round] span. (b) also

satisfies this constraint. In this form, there are two adjacent spans but they are

not adjacent spans of the feature [round]; the span (somun) is a [round] span but

the span (!m) lacks the feature [round]. (In effect, there is a zero span.) Therefore,

the forms in Table 4 tie under the original *A-Span [round] constraint, and as a

result, *A-Span [round] fails to favor total harmony over partial harmony.

Sasa (2008) suggests a revision of one of the assumptions in Span Theory

as an answer to this question, and proposes, first, that the assumption that

segment parsing is exhaustive needs to be revised; that is, GEN should allow

candidates where there are unparsed segments. More specifically, let us assume

that in roundness harmony, round vowels are parsed into a [round] span while

unrounded vowels are not parsed into any span. (22) presents the proposed

output forms for [somun-lar] and *[somun-!m].

(22) The output representations for [somun-lar] and *[somun-!m]

a) [somun-lar] = [(somun)-lar] (the unrounded vowel [a] is unparsed)

b) *[somun-!m] = [(somun)-!m] (the unrounded vowel [!] is unparsed)

Second, let us assume that it is a property of CON whether a candidate

with exhaustive segment parsing wins or not. We can assume that the constraint

in (23), which can be ranked and violable in a grammar, is a replacement of anti-

adjacent span constraints such as the one listed in (21).

(23) Segment Parse [F] (S-Parse [F]) There exists a single span for all vowels such that all the vowels in a domain are parsed into it. (Definition: !(x)"(y) (Vy _Pxy))

Table 5 illustrates the violation and satisfaction of the constraint in (23). As seen

in (23), this S-Parse constraint prefers a candidate in which all of the segments are

exhaustively parsed into a single span. Thus, this constraint enforces (full)

harmony and replaces McCarthy’s original Span-Theoretic constraint *A-Span.

Table 5. Satisfaction and Violation of S-Parse a) [(V V V)] (total harmony) satisfied

- All of the vowels are parsed into a single span.

b) [V V V] (no span) violated once

- The statement in (30) is false because there is no span. c) [(V) V V] (partial harmony) violated once

- There is one span but this span does not contain all of the vowels.

d) [(V) V (V)] (two non-exhaustive spans) violated twice

- There are two spans, neither of which contains all the vowels.

In (23), the feature [F] can be any feature in harmony. Thus, for example,

in roundness harmony, the relevant feature is [round]. In backness harmony, the

relevant feature is [back]. In accounting for roundness harmony, the S-Parse

constraint in (24) enforces total rounding harmony.

(24) S-Parse [round] There exists a single [round] span for all vowels such that all the vowels in a domain are parsed into it.

In addition to the harmony constraint in (24), the following constraints are

necessary to account for the Turkish roundness harmony data. First, it is

necessary to assume a faithfulness constraint that maintains the input-output

identity of the output head segment, as given in (25).

(25) HeadFaith [round] The output head segment is identical to its input correspondent with respect to the feature [round].

The constraint in (25) is a revision of McCarthy’s original FaithHead constraint

(FaithHead [#F]: “If an input segment SI is [#F] and it has an output

correspondent So, then So is a head of an [#F] span” (McCarthy 2004: 5)). The role

of the constraint in (25) is to guarantee that an output head segment (which is

determined by other Span-Theoretic mechanisms) is identical to its input

correspondent in the roundness feature. Thus, for example, if an output head

segment is specified as [round] and its input correspondent is also specified as

[round], then (25) is satisfied. On the other hand, if an output head segment is

specified as [round] but its input correspondent is not specified as [round], or

when an output head segment is not specified as [round], but its input

correspondent is [round], then this head faithfulness constraint is violated.

The directionality of roundness harmony in Turkish is rightward. Thus, a

directionality constraint which designates the leftmost vowel in a span as a head

is also necessary.

(26) SpanHead [round]-L (Span Head-L) (cf. McCarthy 2004: 4) The head of a [round] span is initial in that span. In addition to the Span-Theoretic constraints introduced thus far, the

following OT constraints also play a crucial role in accounting for the roundness

harmony in Turkish; they are listed in (27).

(27) a. Ident I-O [round] (root) (Id (root) [round]) Correspondent input and output segments in the root have the same specification for the feature [round].

b. Ident I-O [back] (root) (Id (root) [back]) Correspondent input and output segments in the root have the same specification for the feature [back].

c. Ident I-O [round] (Id [round])

d. Ident I-O [back] (Id [back])

Correspondent input and output segments have the same specification for the feature [back].

e. *o/Ø

Non-high [round] vowels are prohibited. The positional faithfulness constraints in (27a) and (27b) guarantee the root-

controlled pattern. As will be demonstrated, both the directionality constraint in

(26) and the positional faithfulness constraints are required to capture the root-

controlled pattern observed in Turkish.

2.4.2 The Analysis

First, the tableau in (28) shows the analysis of total roundness harmony.

(28) Total harmony .somun-!m.! Id (root)

[rd] Head Faith

[rd] Span

Head-L *o/Ø

S-Parse [rd]

Id [Rd]

!a) (somun-um)! ! ! ! /! ! /!

b) (somun)-!m * *! c) sam!n-!m *!* * ** d) (somun-um) *(!) *(!) * * In (28), candidate (28d) loses because of either the head faith constraint or the

directionality constraint; in (28d), the head of the [r0und] span is not the initial

vowel in a word, and the roundness specification of the head segment in the

output is not identical to its input correspondent. (28c) violates the root

faithfulness constraint. The remaining two candidates tie under the markedness

constraint, and the segment parsing constraint prefers (28a), the actual form; in

(28a), a single span contains all the vowels while in (28d), there is a span but not

all the vowels are parsed into this span exhaustively. (28) motivates the ranking

Ident [round] (root) >> *o/Ø >> Ident [round].

The analysis of the non-high vowel blocking is shown in (29).

(29) Non-high vowel in the suffix I .somun-lar.! Id (root)

[rd] Head Faith

[rd] Span

Head-L *o/Ø

S-Parse [rd]

Id [Rd]

!a) (somun)-lar! ! ! ! /! /! !

b) (somun-lor) ! ! ! //0! ! /!

c) sam!n-lar /0/! ! ! ! /! //!

Candidate (29c) violates the root faithfulness constraint. The remaining two

candidates satisfy both the directionality constraint and the head faithfulness

constraint. In (29), the markedness constraint is the tie-breaker; *o/Ø prefers the

actual form in (29a) to its competitor, which contains a non-high round vowel in

the suffix. (29) shows that the markedness constraint dominates the segment

parsing constraint: *o/Ø >> S-Parse [round].

(30) gives an additional analysis of the same pattern, but in (30), there is a

non-high round vowel in the suffix in the input. This tableau shows that the

ranking established in (29) predicts the same pattern even when the input is

different.

(30) Non-high vowel in the suffix II .somun-lor.! Id (root)

[rd] Head Faith

[rd] Span

Head-L *o/Ø

S-Parse [rd]

Id [Rd]

!a) (somun)-lar! ! ! ! /! /! /!

b) (somun-lor) ! ! ! //0! ! !

c) sam!n-lar /0/! ! ! ! /! ///!

d) (somun-lor) ! ! /0! //! ! !

In (30), the positional faithfulness constraint rules out (30c), and (30b) loses

because of the markedness constraint. Candidate (30d) satisfies both the root

faithfulness constraint and the head faithfulness constraint; in (30d), the head of

the [round] span is identical to its input correspondent in the roundness

specification. However, this candidate is excluded because of the directionality

constraint. As a result, the actual form in (30a) is selected even when there is a

non-high round vowel in the suffix in the input.

Finally, in (31), both of the vowels are non-high in the root and in the

suffix.

(31) Non-high vowel in the suffix III .son-lar.! Id (root)

[rd] Head Faith

[rd] Span

Head-L *o/Ø

S-Parse [rd]

Id [Rd]

!a) (son)-lar! ! ! ! /! /! !

b) (son-lor) ! ! ! //0! ! /!

c) san-lar /0! ! ! ! /! /!

(31c) loses because of the root faithfulness constraint. (31) shows that the ranking

*o/Ø >> S-Parse [round] successfully selects the attested form in (31a) over (31b).

The ranking summary for the Span-Theoretic analysis is given in Figure 9.

Ident (root) [round] SpanHead-R Head Faith [round] *o/Ø S-Parse [round] Ident [round] Figure 9. Ranking Lattice: Turkish/Span Theory

Figure 9 shows that the blocking effect is expressed in a similar way as in the

feature linking and in the ABC analyses; the ranking *o/Ø >> S-Parse [round] is

analogous to the ranking in which the markedness constraint dominates the

harmony constraint (Spread in the feature linking analysis, and Ident VV [round]

in the ABC analysis).

To summarize, as far as roundness harmony is concerned, Span Theory is

capable of predicting the attested patterns in Turkish, as the other approaches

do. However, as mentioned, in Turkish, there is not only roundness harmony

but also backness harmony. In the next section, I present a Span-Theoretic

treatment of both backness and roundness harmony.

2.5 Discussion

2.5.1 Accounting for Two Harmony Processes

Thus far, I have demonstrated that all three approaches examined in this

chapter successfully predict the attested patterns in roundness harmony. It has

been also shown that both the feature linking analysis and the ABC analysis

successfully account for both roundness harmony and backness harmony.

However, the Span-Theoretic mechanisms established in the previous section are

not sufficient to account for both of the harmony processes. This is illustrated in

(32), where the faithfulness constraints for backness are included instead of those

for roundness. (In (32) and subsequent tableaux, the figure ! designates an

actual surface form which, however, loses in a competition. A bomb (")

designates a candidate which is incorrectly selected as a winner.)

(32) Roundness AND backness harmony .son-ler.! Id (root)

[back] Head Faith

[round] Span

Head-L *o/Ø

S-Parse [round]

Id [back]

!a) (son)-lar! ! ! ! /! /! /0!

b) (son-lor) ! ! ! //0! ! /!

"c) (son)-ler ! ! ! /! /! !

(32b) loses because of the markedness constraint *o/Ø, even though segment

parsing in this candidate is exhaustive. The difference between the remaining

candidates is that (32a) contains a [+back] vowel in the suffix, while in (32c), the

suffix vowel is [-back]. These two candidates tie under the segment parsing

constraint, for in both of the candidates, the span does not contain all the vowels.

The faithfulness constraint, then, prefers (32c) to (32a). As a result, the

mechanism established thus far fails to account for backness harmony.

I suggest that this problem in (32) can be resolved if we assume multiple

spans, as illustrated in (33).

(33) Multiple span representations: candidate (32a) and (32c) in (32)

(32a) (32c) ((son)r-lar)b ((son)r)b-ler

In (33) and throughout, the subscript r is used to indicate a [round] span and b is

used to indicate a [+back] span. The representation in (32a) indicates that the

[+back] span contains both the root vowel and the suffix vowel. Therefore, both

of the vowels are [+back]. The [round] span, however, does not contain the

suffix vowel. (32c), on the other hand, indicates that neither the backness span

nor the [round] span contains the suffix vowel. As a result, the suffix vowel is not

identical to the root vowel either in backness or in roundness.

However, a question arises; is it possible to assume representations such

as (32a)? McCarthy claims that GEN does not create overlapping spans, and one

might claim that both in (32a) and in (32b), two spans, one for roundness and the

other for backness, are overlapping. It is true that McCarthy assumes that

overlapping spans of the same distinctive feature are not allowed. At the same

time, however, McCarthy (2004:3) also claims that “there are different spans for

each distinctive feature,” which suggests that the representations presented in

(32a) are possible in Span Theory; there are two spans in (32a) and in (32b), but

these spans are for different features. Therefore, I assume that the

representations as in (32a) are permissible in Span Theory, and the Span-

Theoretic constraint in (34) enforces complete backness harmony in Turkish.

(34) S-Parse [back] There exists a single [$back] span for all vowels such that contains all the vowels in a domain are parsed into it.

(35) illustrates the analysis incorporating (34). (In (35) and subsequent tableaux,

the figure # designates an actual surface form that wins as a result of

introducing new constraints or mechanisms (that is, problem solved).)

(35) Roundness AND backness harmony .son-ler.! S-Parse

[back] Head Faith

[rd] Span

Head-L *o/Ø

S-Parse [rd]

Id [back]

#a) ((son)r-lar)b! ! ! ! /! /! /0!

b) ((son-lor))rb ! ! ! //0! ! /!

c) ((son)r)b(-ler)b /0/! ! ! /! /! !

(In (35), the root faithfulness constraint is not included due to space limitations.) In (35b), two spans completely overlap, and thus, this candidate satisfies both of

the segment parsing constraints. However, this candidate is excluded because of

the markedness constraint *o/Ø. (35c) violates the segment parsing constraint

because there are two backness spans that do not contain all the vowels. (35a), in

which all the vowels are exhaustively parsed into a single [+back] span, satisfies

*S-Parse [back].

Thus, Span Theory is capable of accounting for both backness and

roundness harmony in Turkish. Let us now turn to a discussion of disharmonic

roots, which is presented in the next section.

2.5.2 Disharmonic Roots

In Turkish, there are disharmonic roots, in which not all of the vowels

agree in backness. Examples of disharmonic roots are given in (36).

(36) Disharmonic Roots (Clements and Sezer 1982: 223, Kirchner 1993: 2)

a. kudret ‘power’

b. anne ‘mother’

c. fiat ‘price’

d. mezat ‘auction’

In (36a) and (36b), the vowel in the first syllable of the word is [+back], but the

vowel in the second syllable is [-back]. In (36c) and (36d), the vowel in the first

syllable is [-back] while the following vowel is [+back]. According to Kirchner

(1993), the vowels in suffixes agree with the last vowel in the root when they are

attached to a disharmonic root. That is, when a suffix is attached to the root in

(36a) and (36b), the suffix vowel is [-back]. The suffix vowel is [+back] when a

suffix is attached to a root in (36c) and in (36d).

The existence of the disharmonic roots does not affect the analysis of

Turkish presented thus far; the Span-Theoretic analysis is presented in (37).

(37) The Span-Theoretic analysis /kudret-a/ Id (root)

[back] S-parse [back]

S-parse [round]

Id [back]

!a) ((ku))rb(dret-e) b ** * * b) ((ku))rb(dre) b(ta) b ***! * c) ((ku)rdra-ta) b *! * * d) (k!drata) b *! ** Candidates (37c) and (37d) satisfy the segment parsing constraint for backness; in

these candidates, all the vowels are parsed into a single [+back] span. However,

these candidates lose because of the root faithfulness constraint. The fully faithful

candidate in (37b) incurs more violations of S-Parse [back] than the actual form in

(37a); there are two non-exhaustive backness spans in (37a), while (37b) contains

three non-exhaustive backness spans. Thus, the ranking Ident (root) [back] >> S-

Parse [back] selects the attested form in the Span-Theoretic analysis.

The analysis with Spread [back] is presented in (38). In (38), (38c) loses

because of the high-ranked positional faithfulness constraint for the root. Under

the spreading constraint (38a), the actual form, is preferred to (38b); (38a) incurs

three violations for Spread [back]: two violations for the [+back] feature of the

initial vowel missing two following vowels (two violations) and the [-back]

feature missing the initial vowel (one violation). (38b) incurs six violations for this

spreading constraint; each backness feature fails to link to two vowels, which

gives rise to six violations (3 features x 2 unlinked vowels). Thus, (38) shows that

the ranking presented in (16) accounts for the harmony pattern when a suffix is

attached to a disharmonic root.

(38) Disharmonic root: /kudret-a/_[kudret-e] /kudret-a/ Id [back] (root) Spread [back] Id [back]

!a) k u dret-e # [+back] [-back]

b) kudret-a #!!!!!!#!!!!#!*+bk] [-bk][+bk]

****!**

c) kurat-a [+back]

Finally, the ABC analysis of disharmonic roots is presented in (39).

(39) Disharmonic roots: ABC Analysis /kudret-a/ Id [back]

(root) Corr V-V Id VV

[back] Id

[back]

!a) kuxdrext-ex * * b) kuxdrext-ax **! c) kuxdraxt-ax *! * d) kuxdret-ax *! (39c) loses because of the root faithfulness constraint, and (39d) loses because of

the correspondence constraint; in this candidate, the medial vowel [e] is not in

correspondence with the other vowels. The Ident VV [back] constraint favors

(39a), the actual form, over its competitor (39b). (39a) violates this output identity

constraint once for the [ux...ex] pair. (39b), on the other hand, incurs two

violations for this identity constraint for the [ux...ex] pair and the [ex...ax] pair.

Hence, the actual form (39a) better satisfies Ident VV [round] and as a result, this

candidate is selected as optimal.

2.5.3 Summary of the Chapter

As seen in this chapter, all three of the approaches considered, feature

linking, Span Theory, and ABC, successfully account for the attested harmony

patterns in Turkish. This suggests that both Span Theory and ABC are the

possible ways to account for vowel harmony, even though these two

approaches were originally proposed to account for consonant harmony. Then,

the next question is whether all of these approaches can successfully account for

other harmony patterns. To investigate this question, another case study, but

with data from Pulaar ATR harmony, is presented in the following two chapters.

Both spreading and ABC are able to correctly account for the attested

backness and harmony patterns observed in Turkish. As seen in this chapter, no

revision or modification is necessary for these approaches. The comparison

between these two approaches is also discussed in Chapter 4 and 5.

Span Theory is also capable of accounting for the Turkish pattern, but as I

showed in this chapter, some revisions of the theory are necessary to achieve

this result. The main focus of Chapter 3 is an examination of Pulaar ATR

harmony in Span Theory. The same revised mechanisms are assumed in

presenting the analysis of Pulaar ATR harmony. I will show, however, that Span

Theory encounters a problem when it is applied in Pulaar ATR harmony.

CHAPTER III HARMONY PATHOLOGIES:

SOUR GRAPES IN PULAAR ATR HARMONY

In Chapter 2, I demonstrated that three approaches, feature linking, Span

Theory, and ABC, successfully account for the data from Turkish backness and

roundness harmony. The main purpose of this chapter and the next chapter is to

investigate whether these three approaches account for a different type of

harmony, that is, data from Pulaar (Niger-Congo) ATR1 harmony; this chapter

concentrates on the Span-Theoretic treatment of Pulaar ATR harmony. I present

the Span-Theoretic account of Pulaar with emphasis on directionality and

harmony pathologies.

The data from Pulaar ATR harmony are difficult to handle because of two

empirical problems: directionality and Sour Grapes. The latter, Sour Grapes,

pointed out by Padgett (1997), has come to the attention of those investigating

vowel or consonant harmony. It is included as one of the harmony pathologies

discussed by Wilson (2006). The term ‘harmony pathology’ "#$#"%!to a situation

in which unwanted or unwelcomed harmony patterns are predicted by the

constraints and/or ranking permutations in Optimality Theory. In this chapter,

the directionality problem and the Sour Grapes problem are illustrated with data

from Pulaar ATR harmony.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 Advanced Tongue Root (Ladefoged 1964, Lindau 1975)

The organization of this chapter is as follows; in Section 3.1, the Pulaar

ATR data are presented. In Section 3.2, the Sour Grapes and directionality

problems are illustrated using data from Pulaar. The Span-Theoretic analysis of

Pulaar ATR harmony is presented in Sections 3.3 and 3.4. 2

3.1 Pulaar Data

Pulaar (also known as Fula or Fulfulde) is a Niger-Congo language

spoken in Senegal, Gambia, (east) Nigeria and (west) Cameroon (McIntosh 1984:

1). Pulaar is known for its [ATR] harmony, where the rightmost vowel (the

vowel in the last syllable) determines the [ATR] specification of the other vowels

in a word. The vowel inventory of Pulaar is presented in Table 6.

Table 6. Pulaar Vowel Inventory Front ([-back]) Back ([+back])

High [+ATR] i u

Mid [+ATR] e o

[-ATR] ´ ø

Low [-ATR] a

Source: Paradis, Carole (1992). Lexical Phonology and Morphology: The Nominal Classes in Fula. New York: Garland Publishing, Inc. In Table 6, and in the explanation of the data, I employ the labels [+ATR] and [-

ATR]. However, the use of a binary feature is solely for explanatory purposes.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!2 The same problems with Span Theory are also discussed in Finley (2008), but in

a different fashion (that is, not with data from Pulaar (or from any other natural language)).

The issue of [ATR] privativity or binarity is discussed later in this chapter (where

the Span-Theoretic analyses are presented) and in Chapter 4.

As seen in the inventory in Table 6, in Pulaar, high vowels are always

[+ATR]; in addition, there are no [+ATR] low vowels in the inventory. Only mid

vowels change their ATR specification depending on the [ATR] specification of

the following vowel.

Pulaar ATR harmony exhibits two patterns: leftward directionality and

low vowel opacity. The full analysis of Pulaar ATR harmony, including the

analysis of opacity, is presented in Chapter 4. In this chapter, I concentrate on the

analysis of leftward directionality. The data in (1) show the basic harmony

pattern. (In the presentation of the data, I follow the transcription system which

is employed in Paradis (1992) except for long vowels, for which I use the long

vowel diacritic instead.) In each form in (1), a root is followed by different

suffixes in the +ATR form and in the -ATR form.

(1) Basic [ATR] Harmony Pattern in Pulaar (Total Leftward) (Paradis 1992: 87) !! &ATR form -ATR form Gloss a. ser-du s´r-øn ‘rifle butt-sg.’ / ‘rifle butt- dim.pl.’

b. pe…c-i p´…c-øn ‘slits-class’ / ‘slits-dim.pl.’

c. dog-o…-ru døg-ø-wøn 'runner-ag.nom.-class’ / ‘runner- nom.-dim.pl.’ In (1), in both the +ATR and -ATR forms, all the vowels in a word exhibit the

same [ATR] specification. The ATR specification of the vowel(s) in the root or in

the medial suffix (as in (1c)) depends on the ATR specification of the vowel in the

word-final suffix; in +ATR forms, since the vowel in the word-final suffix contains

a [+ATR] vowel, all the vowels in a word surface as [+ATR]. Likewise, in -ATR

forms, all the vowels in a word surface as [-ATR] because of the [-ATR] vowel in

the word-final suffix.

In addition to total harmony, partial harmony is also observed in Pulaar.

The examples in (2) illustrate the partial leftward harmony pattern.

(2) Leftward Directionality 1 (Paradis 1992: 87) ! ! -ATR form +ATR form Gloss

a. ı´t-d´ ıet-ir-d´ '()!*#+,-.!/!'()!*#+,-!*+(-.!

(*ı´t-ir-d´, *ıet-ir-de)

b. h´l-d´ hel-ir-d´ ‘to break’ / ‘to break with’ (*h´l-ir-d´, *hel-ir-de)

c. àøkk-ø àokk-ià-à´ ‘one-eyed person’/’to become one-eyed’ (*àøkk-ià-à´,* àokk-ià-àe)

d. f´y’y’-a fey’y’-u-d´ ‘to fell (imperfect)’/’to fell’ (*f´y’y’-u-d´, *fey’y’-u-de) !

In (2), there are high [+ATR] vowels word-medially, and these high vowels affect

the ATR specification of the preceding mid vowel.3 In -ATR forms, a root is

followed by a suffix that contains a [-ATR] vowel, while in the [+ATR] forms, a

root is followed by two suffixes.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3 In the data in (2), the symbol y’ represents a voiced palatal implosive (Paradis

1992: 103).

The root vowel in the +ATR forms surfaces as [+ATR] because of the

[+ATR] vowel in the medial suffix (/-ir-/ in (2a) and (2b), /-id-/ in (2c), and /-u-/

in (2d)). However, the [+ATR] vowel in the medial suffix does not change the

[ATR] specification of the vowel in the word-final suffix; in (2), the word-final

suffix contains a [-ATR] vowel. Thus, (2) shows that directionality of ATR

harmony is only leftward, and the medial vowel, which is specified as [+ATR],

does not affect the ATR specification of the vowel in the word-final suffix.

Another set of examples illustrating leftward directionality in Pulaar is

presented in (3); in (3), the trigger of harmony is the final vowel of the word.

(3) Leftward Directionality 2 (Paradis 1992: 94, 218) !a. binnd-ø…-wø (*binnd-o…-wo, *binnd-o…-wø) ‘writer’

b. baro…-di (*barø…-di) ‘lion’

c. baro-gel (*barø-g´l, *barø-gel) ‘lion-dim’! !

In (3), the word-medial mid vowel agrees with the following vowel in [ATR]

specification; in (3a), for example, the word-medial mid vowel surfaces as

[-ATR] because the vowel in the word-final suffix contains a [-ATR] vowel.

Likewise, the mid vowels in (3b) and (3c) surface as [+ATR] because the

following vowel is specified as [+ATR]. In all of the forms in (3), the preceding

vowel does not affect the [ATR] specification of the medial mid vowel. Thus, the

examples in (3) also show leftward directionality in harmony; if there is a medial

mid vowel, which can change its [ATR] specification, it is always the following

vowel that determines that medial vowel’s [ATR] specification.

To summarize, in Pulaar, only mid vowels change their ATR specification.

The high vowels are always [+ATR] and the low vowel is always [-ATR]; these

specifications never change. Second, the ATR specification of the mid vowels is

predictable expect in word-final position. Finally, the ATR specification of the

non-final mid vowels depends on the ATR specification of the following vowel;

that is, mid vowels surface as [+ATR] when they are followed by a [+ATR]

vowel, and they surface as [-ATR] if they are followed by a [-ATR] vowel.

The Pulaar data presented thus far present one empirical problem for the

existing approaches of harmony, namely, directionality, and none of the current

theories or frameworks, as originally proposed, can successfully handle this

problem. The next section illustrates the directionality problem in Pulaar along

with the Sour Grapes problem, using the data from Pulaar ATR harmony.

3.2 Empirical Issues

! As discussed in Chapter 1, several approaches have been proposed to

account for the harmony facts observed cross-linguistically, but none of them in

the original form, is empirically sufficient to provide analyses of the diverse

harmony patterns found in languages of the world. The data from Pulaar ATR

harmony are especially challenging since the existing frameworks encounter two

empirical problems: Sour Grapes and directionality. The main purpose of this

section is to illustrate these two problems using Pulaar data (to show that these

problems do exist in actual languages). For explanation and demonstration

purposes, I use Spread [ATR], and assume binary [ATR]. The solutions to the

problems are presented as follows; the Span-Theoretic treatments of these

problems are developed in Section 3.3 of this chapter. The solutions by spreading

and ABC are presented in Chapter 4.

3.2.1 Sour Grapes

The Sour Grapes problem refers to the situation in which harmony or

assimilation is predicted to be either all or nothing. More specifically, when all the

segments in a domain can participate in harmony or an assimilatory process,

harmony is total. If, on the other hand, there is a blocker in a domain, a

candidate with no harmony at all is selected as optimal. In other words, when

there is a blocker of harmony present, candidates with partial harmony lose to

the candidate with no harmony.

To illustrate this problem with Pulaar data, I present a preliminary

analysis with the harmony constraint Spread [ATR]. The spreading constraint is

given in (4). In this section, the feature ATR is assumed to be binary, but only for

the sake of presentation and illustration.

(4) Spread [ATR] (cf. Padgett 1997, 2002) If a feature [+ATR] or [-ATR] is associated with a vowel, the same [ATR] feature is linked to all of the vowels in a word.

In addition to (4), the following two constraints are also included in the

analysis; (5) is a markedness constraint that bans [+high, -ATR] vowels, which

are not observed in Pulaar.

(5) *ˆ/¨ (Archangeli and Pulleyblank 1994, Bakovic 2000, Kr0mer 2001)! High vowels are [ATR]. (6) is a faithfulness constraint requiring that input-output correspondents have

the same specification for [ATR].

(6) Ident [ATR] (Id [ATR]) (McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [ATR].

The analysis with (4) through (6) is presented in (7). In (7), there are no

blockers, and all or both vowels surface as [ATR].

(7) Total harmony: NO blocker /s´r-du/ *ˆ/¨ Spread [ATR] Id [ATR]

! a) ser-du [+ATR]

b) s´r-du 1!!!!!!1![-ATR][+ATR]

c) s´r-d¨ 2!!/! [-ATR]

In (7), candidate (7a), the attested form, wins over (7b), where ATR harmony is

not observed. (7) shows that the ranking Spread [ATR] >> Ident [ATR] selects the

candidate with harmony.

However, in (8), the system established in (7) fails to select the actual

form. In (8), there is a blocker, [a], which does not participate in the harmony.4

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4 There is another possible candidate in (8), which is *[bæro…di], in which all the

vowels are [+ATR]. This totally satisfies the agreement constraint, but I assume that such a candidate is excluded by the markedness constraint *æ (no [+low, ATR] vowels), which is undominated in Pulaar.

(8) No harmony: Blocker /barø…-di/ *ˆ/¨ Spread [ATR] Id [ATR]

!a) baro:-di [-ATR] [+ATR]

" b) barø…-di [-ATR] [+ATR]

c) barø…-dˆ [-ATR]

In (8), candidate (8c) loses because of the markedness constraint. The remaining

two candidates, (8a) and (8b), tie under Spread [ATR], and the faithfulness

constraint prefers (8b). As a result, an unattested candidate with no [+ATR]

harmony/spreading is selected as optimal in (8).5

(7) and (8) show that the analysis with Spread predicts all or nothing: if

there is no blocker (that is, all the vowels participate in harmony, as in (7)),

Spread prefers a candidate with (more) complete harmony. However, if there is

a blocker, as in (8), Spread fails to enforce harmony and to discriminate between

a candidate with more harmony, that is (8a), and a candidate with no harmony,

namely (8b). As a result, the candidate with nothing (no harmony) is preferred

because of the faithfulness constraint.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5 In (7) and (8), I used the markedness constraint to exclude a candidate with a

high non-ATR vowel. However, the same result can be achieved with a positional faithfulness constraint for the vowel in the final syllable. The word-final faithfulness constraint is introduced in (9).

3.2.2 Directionality

The other major empirical problem presented by the Pulaar data is

directionality. In previous literature, it is often argued that directionality can be

attributed to other independent phonological phenomena, such as positional

faithfulness. I suggest that such a claim is true in the sense that positional

faithfulness plays a crucial role in accounting for harmony by preserving the

input-output identity of the trigger. The data from Pulaar show, however, that it

is not possible to attribute directionality entirely to positional faithfulness,

thereby abandoning directionality completely. To investigate this issue, another

(preliminary) case study of Pulaar is presented with Spread.

In Pulaar, the positional faithfulness constraint in (9) is assumed to

preserve the input-output identity of the trigger, which is the vowel in the final

syllable of the word (or the final vowel in the word).

(9) Ident I-O [ATR] Word-Final (Id [ATR] (Fin)) (Petrova et al. 2000, 2006: 17; Kr03#" 2001; Walker 2001)

A vowel in the final syllable of a word has the same specification for the feature [ATR] as does its input correspondent.

The analysis with (9) and the constraints in (4) through (6) is presented in

(10). Binary [ATR] is assumed in this section as well. In (10), the actual surface

form is (10a). However, there is no way to successfully select this candidate over

the candidate in (10b).

(10) /binnd-o…-wø/_ [binnd-ø…-wø]4 Spread fails to predict leftward directionality /binnd-o…-wø/ *ˆ/¨ Ident [ATR]

(fin) Spread [ATR]

Id [ATR]

!a) binnd-ø…-wø [+ATR] [-ATR]

"b) binnd-o…-wø [+ATR] [-ATR]

c) binnd-o…-wo [+ATR]

d) bˆnnd-ø…-wø [-ATR]

!In candidate (10c), where all the vowels surface as [+ATR], is excluded by the

positional faithfulness constraint for the vowel in the final syllable. (10d), where

all the vowels surface as [-ATR], loses because of the markedness constraint

against [+high –ATR] vowels.

The remaining candidates are (10a) and (10b), and the crucial difference

between these two candidates is the directionality of harmony. In (10a), the

actual surface form, leftward directionality is observed, and the medial mid

vowel surfaces as [-ATR]. In (10b), the directionality is rightward and the medial

vowel surfaces as [+ATR], agreeing with the preceding [+ATR] vowel in the root.

However, the spreading constraint fails to discriminate rightward and leftward

directionality, and in fact, (10a) loses because of the general faithfulness

constraint for the [ATR] feature, Ident [ATR].

Notice that in (10), both (10a), the actual surface form, and (10b) satisfy the

positional faithfulness constraint. Thus, the positional faithfulness constraint is

silent with regard to these candidates, and therefore, fails to function as a tie-

breaker between (10a) and (10b). Thus, (10) suggests that directionality cannot

simply be attributed to other phonological phenomena, such as positional

faithfulness. If the positional faithfulness constraint is satisfied, a non-directional

harmony constraint, such as Spread [ATR], fails to discriminate between different

directionalities.

To summarize the discussion up to this point, the data from Pulaar ATR

harmony present two challenges: Sour Grapes and directionality. This suggests

that it is necessary to assume that the existing theory must be supplemented

with some additional mechanisms, or to introduce a new theory to handle these

problems as observed in Pulaar. In the next section, I present the Span-Theoretic

analysis, and show how Span Theory handles these problems. It is demonstrated

that Span Theory can handle the attested Pulaar data, but only with the

assumption of privative [ATR].

3.3 Span Theory and Privative [ATR]

In the previous section, I outlined the empirical challenges that the data

from Pulaar present for analyses using the existing theories. This section and the

next section consider whether the Span Theory of harmony can deal with these

two challenges presented by Pulaar. First, in this section, I present the Span-

Theoretic analysis assuming privative [ATR], and in the next section (Section 3.4),

I discuss the Span-Theoretic approach to Pulaar harmony under the assumption

of binary ATR.

In Chapter 2, I presented a modification of Span Theory so that it can be

applicable to vowel harmony, where some features are assumed to be privative.

In this section, I adopt the modification proposed in Chapter 2, and employ the

revised version of Span Theory. One of the modifications of the theory

introduced in Chapter 2 is that the theory allows unparsed vowels; this means

that with privative [ATR], vowels that are not parsed into an ATR span surface

and are realized as non-ATR. Following this modification, I introduce the

following Span-Theoretic constraint to enforce harmony.

(11) Segment Parse [ATR] (S-Parse [ATR]) (Sasa 2008) There exists a single [ATR] span for all vowels such that all the vowels in a domain are parsed into it.

Definition: !(x)"(y) (Vy_Pxy): x=span, y=vowel “There exists a single x (x is a span) for all y (y is a vowel) such that all y are parsed.” The S-Parse constraint is satisfied when all the vowels in a domain are parsed

into a single span. The assessment of (11) is presented in Table 5 in Chapter 2.

(12) is the Span-Theoretic faithfulness constraint which maintains the

input-output identity of the output head segment.

(12) Head Faith [ATR] (Sasa 2008) The output head segment is identical to its input correspondent with respect to the feature [ATR].

The function of (12) is similar to that of positional faithfulness constraints in that

it requires that if a vowel is designated as a head of a span, the input [ATR]

specification of that head vowel must be maintained. The constraint in (12) is a

revision of McCarthy’s original FaithHead [F] constraint (“If an input segment SI

is specified as [F] and it has an output correspondent SO, then SO is the head of an

[F] span” (McCarthy 2004: 5)). The necessity of the revision is discussed later in

this section.

The constraint in (13) determines the location of the head within a span.

(13) SpanHeadR[ATR] (Head-R) (McCarthy 2004: 12) The head segment of an [ATR] span is final in that span.

In addition to the Span-Theoretic constraints in (11) through (13), the

following markedness and faithfulness constraints are also assumed to account

for the data.

(14) *ˆ/¨ (Archangeli and Pulleyblank 1994, Bakovic 2000, Kr0mer 2001) ! High vowels are [ATR]. The markedness constraint in (14) excludes a candidate that contains high non-

ATR vowels, which are not observed in this language.

(15) *e/o (cf. Bakovic 2000)6 No [ATR] mid vowels.

The role of (15) is to prohibit mid [ATR] vowels when [ATR] harmony does not

take place (cf. (17) and (21)).

(16) Ident [ATR] (Id [ATR]) (cf. McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [ATR].

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!6 Bakovic (2000) assumes the markedness constraint *[+ATR] to prohibit mid

[ATR] vowels in unattested positions.

The tableau in (17) shows the analysis of the case in which the word-final

vowel is non-ATR and the preceding mid vowel also surfaces as non-ATR. In (17)

and in subsequent tableaux, it is assumed that when a vowel is not parsed into a

span, such a vowel surfaces as non-ATR. (In this section, the feature [ATR] is

assumed to be privative.)

(17) All non-ATR: /ser-øn/ _ [s´r-øn] /ser-øn/ Head-

R Head Faith [ATR] S-Parse

[ATR] *e/o Id [ATR]

!a) s´r-øn * * b) (ser-on) *! ** * c) (ser-on) *! ** * d) (ser)-øn * *! In (17), candidate (17b) loses because of the directionality constraint; in this

candidate, the head of the span is not the rightmost vowel. Candidate (17c) loses

because of the Head Faith [ATR] constraint; in this candidate, the ATR mid vowel

[o] heads an ATR span. The remaining two candidates, (17a), the actual form, and

(17d), both satisfy the segment parsing constraint, but (17d) loses because of the

markedness constraint against mid ATR vowels. (17) shows the following

ranking arguments: Head-R, FaithHead >> S-Parse [ATR], and *e/o >> Ident

[ATR].7

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7 One might ask the following question with regard to the ranking *e/o >> Ident

[ATR]: how would the system generate ATR mid vowels with the ranking presented in (17) when there are [ATR] mid vowels in the input? There are several possible ways to preserve the input mid [ATR] vowels; there are two faithfulness constraints for the final vowel and for the output head segment, and in addition to this, S-Parse [ATR] prefers [(e)] to [´].

The analysis of full harmony is presented in (18). In (18), the word-final

vowel is [+high], which always surfaces as ATR, and all of the vowels surface as

[ATR].

(18) S-Parse enforces full harmony /s´r-du/ Head-R *ˆ/¨ Head Faith

[ATR] S-Parse [ATR]

*e/o Id [ATR]

!a) (ser-du) * * b) s´r(-du) *! c) s´r-d¨ *! * * !In (18), candidate (18a) is the actual form; the harmony is triggered by the word-

final [ATR] vowel [u], and the vowel in the root undergoes the harmony. (18b) is

the fully faithful candidate, where the final [ATR] vowel forms a span while the

non-ATR vowel in the root is not parsed into an ATR span. There are no spans in

candidate (18c); none of the vowels is parsed into a span in this candidate and all

the vowels in this candidate surface as non-ATR.

Candidate (18c) is excluded either by the markedness constraint against

high non-ATR vowels or by the S-parse constraint. (18b) loses because of the S-

Parse constraint because segment parsing in this candidate is not exhaustive. (18)

shows the following ranking: *ˆ/¨, S-Parse [ATR] >> *e/o, Ident [ATR]. (The

ranking between Head Faith [ATR] and S-Parse [ATR] is established in (17).)

The tableau in (19) presents the analysis of the same case (total harmony),

but there is a non-ATR high vowel in the trigger position in the input.

(19) Headedness and S-parse guarantee that harmony takes place /s´r-d¨/! Head-R *ˆ/¨ Head Faith

[ATR] S-Parse [ATR]

*e/o Id [ATR]

!a) (ser-du)! ! ! 5! ! 5! 55!

b) s´r(-du) * *! * c) s´r-d¨ *! * !(19c) loses because of the markedness constraint *ˆ/¨. Candidates (19a) and (19b)

tie under the head faithfulness constraint, and the S-Parse [ATR] constraint

prefers candidate (19a), the actual form. (19) presents the following ranking

argument: *ˆ/¨ >> Head Faith [ATR].

In the following tableaux in (20) and (21), the analyses for the word-

medial mid vowel case are presented. In (20) and (21), there is a mid vowel

word-medially, preceding a word-final non-ATR mid vowel and following a high

ATR vowel. The medial vowel surfaces as non-ATR. As a result, total harmony is

not observed in this case. (Once again, [ATR] is assumed to be privative in this

section.)

(20) Directionality and headedness constraints block total harmony /bind-o…-wø/ Head-R *ˆ/¨ Head Faith

S-Parse

*e/o Id

!a) (bind)-ø…-wø * *

b) (bind-o…-wo) *! ** *

c) (bind-o…-wo) *! ** *

d) bˆnd-ø…-wø *! * **

!In (20), four candidates are evaluated; (20a) is the actual form, where the high

ATR vowel forms its own span and the rest of the vowels are unparsed. (20b)

and (20c) are the candidates with total ATR harmony, where all the vowels

surface as [ATR]. The difference between these two candidates is the location of

the head; in (20b), the initial (or the leftmost) vowel is the head and in (20c), the

final (or the rightmost) vowel is the head. Finally, (20d) is another total harmony

candidate (in that all of the vowels surface as non-ATR) but in this candidate,

none of the vowels is parsed into an ATR span.

(20b) loses because of the directionality constraint; in this candidate, the

head of the span is not the rightmost vowel in the span. (20d) is excluded by the

markedness constraint prohibiting high non-ATR vowels. One of the remaining

candidates, (20c), is excluded because of the head faithfulness constraint, and as a

result, the actual surface form is selected as optimal in (20). Thus, in this word-

medial mid vowel case, total harmony is unattainable; candidates with total

harmony are blocked either by the directionality constraint or by the head

faithfulness constraint.

Another analysis of the same input is presented in (21), but with a

different candidate set.

(21) Headedness and directionality select the attested directionality /bind-o…-wø/ Head-R *ˆ/¨ Head Faith

S-Parse

*e/o Id

!a) (bind)-ø…-wø * *

b) (bind-o…)-wø *! * *

c) (bind-o…)-wø * *!

d) (bind)(o…-wo) *! ** ** *

!The analysis in (21) shows that in the medial mid vowel case, it is not possible to

parse all the vowels into a single span. In (21), segment parsing is not exhaustive

in any one of the candidates; (21a) is the actual form with two unparsed non-ATR

vowels. Both (21b) and (21c) are realized in the same way but in these two

candidates, the location of the head is different. In (21d), all the vowels are parsed

into spans (and thus, are realized as ATR), but there are two non-exhaustive

spans.

Candidates (21b) and (21d) are excluded by the directionality constraint

and the head faithfulness constraint respectively; in (21b), the location of the

head is not final in the span, and in (21), even though it satisfies the directionality

constraint, the input specification of the [ATR] feature is not maintained in the

output head segment. The remaining two candidates, (21a) and (21c), satisfy all

of *ˆ/¨, Head-R, and Head Faith [ATR], and they tie under the segment parsing

constraint. However, the markedness constraint *e/o excludes candidate (21c).

Both (20) and (21) show that Head [ATR]-R and Head Faith [ATR] play a crucial

role in predicting the attested directionality. These two constraints also block the

candidate with total harmony in the word-medial mid vowel case.

Finally, the analysis of the word-medial trigger case is presented in (22).

(22) shows, however, that the mechanism that has been established thus far fails

to account for this case.

(22) Word medial trigger : /h´l-ir-d´/_[hel-ir-d´] /h´l-ir-d´/ Head-R *ˆ/¨ Head Faith

[ATR] S-Parse [ATR]

*e/o Id [ATR]

!a) (hel-ir)-d´ * *! * b) h´l(-ir-de) *! * * * c) h´l-ˆr-d´ *! * * "d) h´l-´r-d´ * *

In (22), the actual surface form is (22a), in which the mid vowel surfaces as [ATR]

because of the following [ATR] high vowel. In (22b), rightward directionality is

observed, and the word-medial [ATR] vowel triggers the harmony to the

following vowel. In (22c), all of the vowels surface as non-ATR. All of the vowels

surface as non-ATR in (22d) as well, but in this candidate, vowel lowering is

observed and the word-medial surfaces as non-high.

Candidate (22b) loses because of the directionality constraint, and (22c)

loses because of the markedness constraint *ˆ/ .̈ Both of the remaining

candidates, (22a) and (22d), equally violate the segment parsing constraint, and

the markedness constraint *e/o is the tie-breaker. As a result, (22d) is wrongly

selected as optimal because of the markedness constraint.

The problem with (22d) is that vowel lowering is observed to satisfy the

headedness constraint for high vowels. However, such a change is not observed

in Pulaar; to block such an unattested change, I suggest the faithfulness

constraint in (23).

(23) Ident [high] (Id [high]) (McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [high].

The solution with (23) is presented in (24); (24) shows that the faithfulness

constraint for vowel height must dominate the markedness constraint *e/o.8

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!8 In (24), there is one more possible candidate, *[h´l(-ir)-d´]. This candidate

satisfies the directionality, markedness, and head faithfulness constraints, and in fact, the markedness constraint favors this candidate over the actual form. I

(24) Word medial trigger : /h´l-ir-d´/_[hel-ir-d´] /h´l-ir-d´/ Head-R *ˆ/¨ S-Parse

[ATR] Id

[high] *e/o Id

!a) (hel-ir)-d´ * * * b) h´l(-ir-de) *! * * * c) h´l-ˆr-d´ *! * * d) h´l-´r-d´ * *! * Figure 10 shows the summary of the rankings established thus far. As

indicated in Figure 10, in Pulaar, the Head [ATR]-R and Head Faith [ATR]

constraints, both of which are ranked above S-Parse [ATR], are active in the

grammar; that is, unless the directionality and head faithfulness constraints are

satisfied, total harmony is unattainable in Pulaar.

! *ˆ/¨ Head [ATR]-R ! Head Faith S-Parse [ATR] Ident [high] *e/o Ident [ATR]

Figure 10. Ranking Lattice: Pulaar/Span Theory The directionality constraint bans the candidate in which unattested rightward

directionality is observed. Along with the directionality constraint, the head

faithfulness constraint is also active to prohibit unattested harmony; harmony is

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!assume, however, that this candidate is excluded by another segment parsing constraint, *Unparse. This constraint is introduced in (29) in this section.

! 100!

observed only when the input-output identity of the [ATR] specification is

maintained in the output head segment. This reformulated head faithfulness

constraint plays a crucial role to guarantee the attested harmony pattern.

Thus far, Span Theory successfully accounts for the attested data in Pulaar

with the assumption of privative ATR. There are, however, two residual issues.

First, in the analysis, the revised version of McCarthy’s FaithHead constraint was

used. (25) presents the original formulation of FaithHead, when it is applied to

ATR harmony.

(25) FaithHead [ATR] (cf. McCarthy 2004: 5) If an input segment SI is specified as [ATR] and it has an output correspondent SO, then SO is the head of an [ATR] span.

(26) illustrates the analysis of the case with no harmony with this original

FaithHead constraint.

(26) /s´r-øn/ _ [s´r-øn]: No ATR vowel, all non-ATR /s´r-øn/ *ˆ/¨ Head-R FaithHead

[ATR] S-Parse [ATR]

!a) s´r-øn # *! b) (ser-on) *! # ** "c) (ser-on) # ** !In (26), both (26a) and (26b) satisfy FaithHead [ATR] if privative ATR is assumed;

the original formulation in (25) states that if an input vowel is specified as ATR,

then, its output correspondent is ATR (and heads an ATR span). However, in

(26), none of the vowels in the input is specified as ATR, so (25) is vacuously

satisfied. (26a), the actual form, violates the segment parsing constraint while

(26c) satisfies this constraint. Under the markedness constraint, (26c) is worse

! 101!

than (26a), but as discussed, the ranking S-Parse [ATR] >> *e/o must be

established. Thus, it appears that the revised Head Faith constraint is a necessary

revision to the theory so that the identity of the head segment is guaranteed

even when a privative ATR feature is assumed.

Second, even with the established system and the revision of the theory,

the Sour Grapes problem is not resolved in Span Theory. This is illustrated in

(28), where the form in (27) below is examined:

(27) Leftward Directionality (Repeated from (3c)) (Paradis 1992: 94, 218) baro-gel (*barø-g´l, *barø-gel) ‘lion-dim’

In the form in (27), there is a mid vowel word-medially ([o]), and this mid vowel

agrees with the following mid vowel [e] in its ATR specification. The preceding

low vowel does not participate in the harmony, nor does it affect the ATR

specification of the word-medial mid vowel. Recall that in Pulaar, a low vowel is

always non-ATR, and there are no [+low, ATR] vowels. This is enforced by the

markedness constraint *æ (no [+low, ATR] vowels), which is included in (28).

(28) Sour Grapes4!/67"ø8,#9/!_!:67")8,#9;!

/barø-gel/ *æ Head-R Head Faith [ATR]

S-Parse [ATR]

Id [ATR]

!a) ba(ro-gel) * *! b) barø-g´l * *! "c) barø(-gel) * d) (bæro-gel) *! !The analysis presented in (28) exhibits the Sour Grapes problem; (28a), which

exhibits more complete harmony, loses to (28b), where no harmony is observed.

! 102!

Notice that there is a blocker in the domain, namely, the low vowel [a]. (28)

shows that Span Theory still encounters the Sour Grapes problem, and the

established system still fails to enforce partial harmony when there is a vowel

that does not participate in harmony.

Sasa (2008) presents the constraint in (29) as a solution to this problem.

(29) *Unparse (Sasa 2008) A vowel is parsed into some span. Assign one violation mark for each non-conforming vowel (“No unparsed vowel”).

Definition: "(x)!(y) ([Parse]y,x]): “For all vowels, there is a span such that a vowel is parsed into it.” The parsing constraint in (29) prohibits an unparsed vowel, and it is fully satisfied

when there are no unparsed vowels in a harmony domain. As the definition of

(29) shows, the quantification of (29) is the reverse of that of the S-parse [ATR]

constraint.

The solution to the Sour Grapes problem is presented in (30).

(30) Sour Grapes solved: /barø-gel/ _ [baro-gel] /barø-gel/ *æ Head-R Head Faith

[ATR] S-Parse [ATR]

*Unparse

Id [ATR]

$a) ba(ro-gel) * * * b) barø-g´l * **!* * c) barø(-gel) * **! In (30), all the candidates violate the *Unparse constraint; however, the actual

form in (30a) satisfies this parsing constraint better than the competitors; (30b),

where there is no harmony at all, incurs three violations for three unparsed

vowels, and (30c) incurs two violations for two unparsed vowels.

! 103!

*Unparse is also necessary in the case in which there is a trigger word-

medially.

(31) Word-medial trigger: /h´l-ir-d´/_[hel-ir-d´] /h´l-ir-d´/ Head-R Head Faith

[ATR] S-Parse [ATR]

*Unparse

Id [ATR]

! a) (hel-ir)-d´ * * * b) h´l (-ir-de) *! * * * c) h´l(-ir)-d´ * **! d) (hel-ir-de) *! ** In (31), candidate (31b) loses because of the directionality constraint. (31d) is

excluded by the head faithfulness constraint, since the head segment is not

faithful to its input correspondent with respect to [ATR]. (31a) and (31c) tie under

the directionality, headedness, and S-Parse [ATR] constraints, and *Unparse

functions as a tie-breaker; in (31a), there is one unparsed vowel while (31c)

contains two unparsed vowels. Thus, (31a) is selected as optimal because of

*Unparse.

To summarize this section, first, the Span-Theoretic analysis successfully

resolves two empirical challenges with Pulaar ATR harmony: directionality and

Sour Grapes. The attested directionality is correctly predicted by i) requiring a

head segment (vowel) to be faithful to its input correspondent with respect to

the [ATR] specification, and ii) designating the rightmost vowel in a span as a

head. This is achieved by two Span-Theoretic mechanisms, the revised head

faithfulness constraint and the directionality constraint. Second, the Sour Grapes

problem is resolved by introducing another type of segment parsing constraint,

! 104!

as in (29); this segment parsing constraint prohibits any unparsed vowels and

achieves more harmony by forcing more vowels to be parsed into (a) span(s).

Therefore, we can conclude that Span Theory can avoid those empirical

problems in Pulaar if the feature [ATR] is assumed to be privative; notice that the

effect of *Unparse is visible only when a feature is assumed to be privative, that

is, when there are unparsed vowels observed in a candidate.

This raises another question: can Span Theory handle these problems

even when a feature is assumed to be binary? The next section discusses this

question by presenting another Span-Theoretic analysis of Pulaar harmony, but

with the assumption of binary [ATR].

3.4 Span Theory and Binary [ATR]

The question that is addressed in this section is, can Span Theory still avoid

the directionality problem and the Sour Grapes problem if the feature [ATR] is

assumed to be binary? To investigate this question, the same data from Pulaar

are analyzed under the assumption of binary [ATR]. Even though this

assumption is different, the same Span Theoretic mechanisms introduced in the

previous section are assumed in the analysis. However, the following two

assumptions are different under binary [ATR]. First, if binary [ATR] is assumed,

[-ATR] vowels are also assumed to form their own spans; that is, the vowels

parsed into a [+ATR] span are realized as [+ATR] and likewise, the vowels parsed

into a [-ATR] span are realized as [-ATR]. Second, if features are binary, there

should be no unparsed vowels, as is proposed in McCarthy’s original

! 105!

presentation of the Span Theory. Therefore, I assume that, if [ATR] is binary, the

parsing constraint in (29) is either not part of the grammar (since McCarthy

claims that GEN does not create candidates with unparsed vowels/segments), or

is undominated in the constraint hierarchy so that it prohibits any candidates

with unparsed segments.

The analysis in (32) is the implementation of these assumptions.9

(32) No [ATR] harmony: /ser-øn/ _ [s´r-øn] /ser-øn/ Head-R Head Faith

[ATR] S-Parse [ATR]

*e/o Id [ATR]

!a) (s´r-øn) * b) (ser-on) *! ** * c) (ser-on) *! ** * d) (ser)(-øn) **! * In (32), the actual form contains a [-ATR] span that contains all the vowels in the

output. Candidate (32b) loses because of the directionality constraint, and (32c) is

excluded because of the faithfulness constraint for the head segment. (32a), the

actual form, better satisfies the segment parsing constraint than (32d), since in

(32a), all the vowels are exhaustively parsed into a single [-ATR] span while in

(32d), there are two non-exhaustive spans. (32) shows the ranking *e/0 >> Ident

[ATR].

(33) presents another analysis of total [+ATR] harmony; (33) presents the

ranking S-Parse [ATR] >> *e/o.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9 Since the purpose of this section is to start laying out another analysis with a

different fundamental assumption (that is, [ATR] is binary), the rankings established in Section 3.3 are discarded in this section.

! 106!

(33) S-Parse enforces full harmony /s´r-du/ Head-R *ˆ/¨ Head Faith

[ATR] S-Parse [ATR]

*e/o Id [ATR]

!a) (ser-du) * * b) (s´r)(-du) *!* c) (s´r-d¨) *(!) *(!) * !(33c) loses because of the markedness constraint against [+high, -ATR] vowels.

(33b) loses because of the segment parsing constraint.

(34) presents the directionality case. In (34), the attested leftward

directionality is still correctly predicted even under the assumption of binary

ATR (that is, the spreading of the [-ATR] feature of the word-final vowel to the

media mid vowel).

(34) Leftward directionality /bind-o…-wø/ Head-R *ˆ/¨ Head Faith

[ATR] S-Parse [ATR]

*e/o Id [ATR]

!a) (bind)(-ø…-wø) * *

b) (bind-o…)(-wø) *! * ** *

c) (bind-o…)(-wø) * *!* *

d) (bind)(o…-wo) *! ** *

!In candidate (34b), the location of the head of the first span is not final in that

span, and this candidate violates the directionality constraint. The head

faithfulness constraint excludes (34d). (34c) satisfies the directionality constraint

and the head faithfulness constraint, but this candidate is ruled out because of the

markedness constraint *e/o. Thus, (34) shows that even with the assumption of

binary [ATR,] Span Theory still successfully predicts the attested directionality

with the same mechanisms (the head faithfulness constraint and the

directionality constraint). (34) also shows that the Sour Grapes problem is

! 107!

avoided in the example presented in (34); the analysis predicts leftward [-ATR]

spreading from the final vowel, as seen in (34a). Notice that there is a blocker in

(34), and the high vowel in the first syllable does not participate in harmony.

However, (35) shows that the Sour Grapes problem is not fully solved.

The analysis presented in (32) through (34) fails to enforce harmony when there

is a low vowel blocker; in (35), the ranking Head Faith [ATR] >> S-Parse [ATR] is

established so that (35b) is excluded.

(35) Sour Grapes4!/67"ø8,#9/!_!:67")8,#9;!(cf. (28) and (30)) /barø-gel/ *æ Head-R Head Faith

[ATR] S-Parse [ATR]

Id [ATR]

!a) (ba)(ro-gel) ** *! b) (barø-g´l) *! * "c) (barø)(-gel) ** d) (bæro-gel) *! ** In (35), candidate (35d) loses because of the markedness constraint against [+low,

+ATR] vowels, and (35b) loses because of the head faithfulness constraint; in this

candidate, the word-final vowel, which is the head of the span, is not identical to

its input correspondent in the [ATR] specification

The remaining two candidates, (35a), the actual form, and (35c) both

equally violate the segment parsing constraint. The competition, then, goes

down to the general faithfulness constraint, and as a result, (35c), the Sour

Grapes candidate is selected over the actual form. This problem cannot be

resolved even if McCarthy’s original *A-Span [ATR] (“Assign one violation for a

pair of adjacent ATR spans.”) and FaithHead [ATR] (“If an input segment SI is

! 108!

specified as [!ATR] and it has an output correspondent SO, then SO is the head of

an [!ATR] span: cf. (25) of this chapter) are assumed; both of these candidates

contain two adjacent spans, and they both equally incur one violation of the *A-

Span [ATR] constraint. The (original) FaithHead [ATR] is also obeyed both in

(35a) and in (35c); in both, the output correspondent of an input [-ATR] vowel is

a head of a [-ATR] span, and the output correspondent of an input [+ATR] vowel

is a head of a [+ATR] span.

In (30), where the same case is examined but under a different

assumption, namely, privative ATR, the key to the solution was the *Unparse

constraint, which prohibits unparsed segments. If binary ATR is assumed,

however, all the vowels are necessarily parsed into either a [+ATR] span or a

[-ATR] span. In other words, the effect of *Unparse is invisible under binary ATR

(or any binary feature) since either GEN does not create a candidate with

unparsed segments, or *Unparse is undominated so that any candidate with

unparsed segments will never be selected as optimal. Therefore, the analysis

presented in (35) suggests that the Span Theory of harmony does not allow a

uniform account of the diverse patterns of vowel harmony because if binarity is

assumed for ATR, it fails to account for the attested data of Pulaar; more

specifically, it fails to resolve the Sour Grapes problem.

To summarize, first, Span Theory successfully avoids the directionality

problem and the Sour Grapes problem as demonstrated in Section 3.2 in this

chapter, if the feature ATR is assumed to be privative. As seen in this section,

! 109!

Span Theory still successfully predicts the attested directionality in Pulaar even

under the assumption of binary ATR, but as seen in (35), it fails to resolve the

Sour Grapes problem if ATR is assumed to be binary. The discussion of the

privativity/binarity of the features in harmony continues into the next section

based on the observations from the Span-Theoretic analysis.

3.5 Discussion

In Section 3.4, I showed that Span Theory crucially requires the

assumption that the feature ATR is privative; as seen in Section 3.4, if ATR is

assumed to be binary, Span Theory fails to resolve the Sour Grapes problem.

This observation leads us to one question: can all the harmonic features be

privative? If all of the harmonic features can be privative, Span Theory can be a

viable theory to account for vowel harmony; as seen in this chapter, Span

Theory successfully solves two empirical problems with the assumption of

privative [ATR]. If, on the other hand, not all harmonic features are be privative,

then Span Theory will encounter a similar problem, as are observed in Pulaar,

when applied in other harmony languages. This, in turn, means that if there are

any harmony patterns that require binary features, Span Theory, which requires

the assumption of privative features, cannot be a viable theory to be used to

account for the diverse vowel harmony patterns.

The question of whether a certain feature is privative or binary hinges on

two factors: i) which value, say, [+ATR] or [-ATR], is more marked, and ii) which

feature is active in harmony/assimilation. For example, in vowel harmony, the

! 110!

feature [round] is assumed to privative, since numerous previous studies,

including Steriade (1995), show that in roundness harmony, the only active

feature is [(+) round], and for non-high vowels (especially, [-back] vowels),

[round] vowels are more marked than unrounded vowels. For example, in

Turkish (presented in Chapter 2), the occurrence of non-high rounded vowels is

more restricted than that of high rounded vowels.

However, such a clear-cut observation cannot be made for all of the

features involved in vowel harmony processes. For example, for the feature

[ATR], it has been widely argued that only [(+) ATR] or [(-) ATR]/[RTR]

(Retracted Tongue Root), but not both, is active in harmony in a single language

(cf. Archangeli and Pulleyblank 1994). However, this does not necessarily mean

that there are no languages where both [+ATR] and [-ATR] are active; for

example, Steriade (1995) points out that Kalenjin (Hall et al. 1974, Ringen 1989) is

one of the languages where both [+ATR] and [-ATR] are required; I suggest in

the next chapter that Pulaar is another language where both [+ATR] and [-ATR]

must be active.10

The feature [back] is even more controversial; if the feature [back] is

assumed to be privative, then which value is more marked or assumed to be

active in harmony? Steriade (1995) mentions that assuming privative [back] will

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!10

It appears that the preliminary analysis presented in Section 3.2 suggests that assuming binary ATR does not solve the directionality and the Sour Grapes problems in Pulaar. However, the solution to these problems is presented in Chapter 4 with the assumption of binary ATR.

! 111!

result in a better analysis of the data in Finnish vowel harmony, where neutral

vowels (vowels that do not participate in harmony; see Chapter 1) are [-back];

Steriade also points out that in Chamorro (Chung 1983), [-back] is the active

feature. Thus, the issue of the privativity or binarity of the feature [back] has not

yet been fully settled.

These observations lead us to conclude that it is not possible to claim that

all harmonic features can be privative. This further suggests that Span Theory,

which crucially relies on the assumption of privative features, cannot be

empirically adequate as a theory to account for vowel harmony; as seen in

Pulaar, Span Theory requires the assumption of privative [ATR] to avoid Sour

Grapes. However, once again, the assumption that all harmonic/assimilating

features are privative cannot be maintained. If Span Theory crucially relies on the

assumption of privative features, then it is predicted that Span Theory will

encounter a similar problem in other languages if a harmony feature is assumed

to be binary.

Hence, on the basis of the discussions presented in this chapter, it is

concluded that Span Theory cannot be a uniform way of accounting for the

diverse harmony patterns in world’s languages (unless all of the harmonic

features can be uniformly privative). Thus, for the remainder of this thesis, I

concentrate on the two remaining approaches: spreading and ABC. In Chapter 4,

I present the spreading and ABC analyses of the Pulaar harmony, and in Chapter

! 112!

5, I present another case study with different harmony processes using data

from Yakut.

! 113!

CHAPTER IV PULAAR ATR HARMONY:

FULL ANALYSES WITH SPREAD AND ABC

This chapter presents full analysis of Pulaar ATR harmony in two

approaches: feature linking with Spread and Agreement-By-Correspondence

(ABC). As demonstrated, both feature linking and ABC successfully account for

the Pulaar data, but these two analyses make different predictions for the data;

the analysis with feature linking suggests that in Pulaar, both [+ATR] and [-ATR]

are active, while for the ABC analysis, such an assumption is not necessary. In

addition to the comparison between two analyses, the role of positional

faithfulness (Beckman 1997, 1998) in harmony is discussed in this chapter.

The organization of this chapter is as follows; Section 4.1 is a review of the

Pulaar harmony data with the addition of data illustrating low vowel opacity.

The full analysis of the data with feature linking with Spread is presented in

Section 4.2, and the ABC analysis is presented in Section 4.3. Section 4.4 is a

general discussion of these two different approaches.

4.1 Review of the Pulaar Data

Some of the Pulaar data presented in Chapter 3 are repeated in (1)

through (3). (The vowel inventory of Pulaar is presented in Table 6 in Chapter 3.)

I use binary [ATR] in the presentation of the data, but the privativity or binarity

of the feature [ATR] is revisited later in this chapter.

! 114!

(1) Basic [ATR] Harmony Pattern in Pulaar (Total Leftward) (Paradis 1992: 87) !! "ATR form -ATR form Gloss a. ser-du s´r-øn ‘rifle butt-sg.’ / ‘rifle butt- dim.pl.’

b. pe…c-i p´…c-øn ‘slits-class’ / ‘slits-dim.pl.’

c. dog-o…-ru døg-ø-wøn 'runner-ag.nom.-class’ / ‘runner- nom.-dim.pl.’ (2) Leftward Directionality 1 (Paradis 1992: 87) ! ! -ATR form +ATR form Gloss

a. ı´t-d´ ıet-ir-d´ #$%!&'()*+!,!#$%!&'()*!&($*+!

(*ı´t-ir-d´, *ıet-ir-de)

b. h´l-d´ hel-ir-d´ ‘to break’ / ‘to break with’ (*h´l-ir-d´, *hel-ir-de)

(3) Leftward Directionality 2 (Paradis 1992: 94, 218) !a. binnd-ø…-wø (*binnd-o…-wo, *binnd-o…-wø) ‘writer’

b. baro…-di (*barø…-di) ‘lion’

c. baro-gel (*barø-g´l, *barø-gel) ‘lion-dim’ In Pulaar, mid vowels agree with the following vowel in ATR specification. In (1),

the same root is realized differently depending on the ATR specification of the

vowel in the suffix; when the suffix contains a [+ATR] vowel, the vowel in the

root is realized as [+ATR], and the root vowel is realized as [-ATR] when the

suffix contains a vowel that is [-ATR]. Clear directionality is another characteristic

of Pulaar harmony; in the [+ATR] form in (2a), the medial [+ATR] high vowel

! 115!

affects the ATR specification of the preceding mid vowel. However, the final

vowel is not affected by the ATR specification of the preceding vowel; it surfaces

as [-ATR]. Likewise, in (3a), the word-medial mid vowel surfaces as [-ATR]

because of the [-ATR] word-final vowel, but the preceding [-ATR] low vowel

does not affect the ATR specification of the medial mid vowel.

Another major characteristic of Pulaar ATR harmony is low vowel

opacity. As seen in (4), the low vowel behaves opaquely.

(4) Opacity (Paradis 1992: 88, Archangeli and Pulleyblank 1994: 136) a. bø…t-a…-ri ‘lunch’ (*bo…t-a…-ri, *bo…t-æ…ri)

b. pø…f-a…ri ‘breaths’ (*po…f-a…-ri, *po…f-æ…ri)

c. ø…n~an-˜gel ‘torsion-dim’ (*go…ıan-˜gel, *go…ıæn-˜gel)

d. k´lan-˜gel ‘cassure-dim’ (*kelan-˜gel, *kelæn-˜gel)!

As mentioned in Chapter 3, the low vowel [a], which is specified as [-ATR], lacks

a [+ATR] counterpart, and always surfaces as [-ATR]. In (4a), for example, the

word-final vowel is a [+high, +ATR] vowel but the spreading of the [+ATR]

feature is blocked by the word-medial low vowel [a], which lacks a [+ATR]

counterpart. As a result, the mid vowel in the root surfaces as [-ATR], agreeing

with the word-medial low vowel, rather than with the word-final [+ATR] vowel,

in [ATR] specification. As seen in (4), vowel length does not affect the opaque

behavior of the low vowel; that is, the low vowel behaves opaquely whether it is

long, as in (4a) and (4b), or short, as in (4c) and (4d).

! 116!

The next two sections present full analyses of the Pulaar ATR harmony

with feature spreading (using Spread) and with ABC. The next section, Section

4.2, presents the feature linking analysis. As shown in Chapter 3, the feature

linking analysis with Spread encounters two problems: Sour Grapes and

directionality. The solutions to these problems are presented in Section 4.2.2.

4.2 Analysis with Spread

4.2.1 Spread Defined

This section (4.2.1) and the next section (4.2.2) present the full feature

linking analysis of Pulaar assuming Spread as a harmony constraint. The OT

constraint Spread [F] was first introduced by Padgett (1997). The original

formulation of Spread [F] in Padgett (1997) is presented in (5).

(5) Spread [F] (cf Padgett 1997: 22) Every feature [F] is linked to every segment. (Spread(x): !xy, x(y) (x; feature, y: segment) (in some domain)) The spreading constraint is satisfied only when all the segments in a domain (for

example, ‘a word’) share the same feature [F].

As demonstrated, however, there are two major problems with the

original formulation of Spread. First, as seen in the Pulaar directionality case, this

non-directional spreading constraint fails to discriminate among candidates that

exhibit different spreading directionalities; for example, in Pulaar, the attested

directionality is leftward, but Spread without specified directionality fails to favor

the candidate with the attested directionality over the unattested one with the

rightward directionality.

! 117!

This problem with directionality gives rise to the second problem, namely,

the Sour Grapes problem. To illustrate this, the analysis presented in (10) in

Chapter 3 is repeated in (6).

(6) /binnd-o…-wø/_ [binnd-ø…-wø] (repeated from (9) in Chapter 3) /binnd-o…-wø/ *ˆ/¨ Id [ATR] (fin) Spread [-ATR] Id [ATR]

!a) binnd-ø…-wø | | [+ATR] [-ATR]

"b) binnd-o…-wø | | [+ATR] [-ATR]

The analysis above was presented to illustrate the directionality problem, but this

also can be seen as the Sour Grapes problem; in (6), where binary ATR is

assumed, the [-ATR] feature associated with the final vowel should also be

associated with the medial vowel. However, in (6), the candidate with no [-ATR]

harmony, namely (6b), is selected if there is a blocker that cannot participate in

[-ATR] harmony.

(6) shows that the analysis using Spread in its original formulation fails to

enforce (more) complete harmony if there is a blocker in a domain; more

specifically, where there is a [-ATR] vowel at the end of a word, which triggers

[-ATR] harmony to a preceding word-medial (alternating) vowel, and a high

vowel (which cannot change to [-ATR]) as an initial vowel, the analysis with

Spread predicts that the medial vowel surfaces as [+ATR]. In other words, if the

original spreading constraint, as in (5), is employed in the analysis, this spreading

constraint fails to enforce harmony if there is a blocker in the domain.

! 118!

These two issues, directionality and Sour Grapes, appear not to be related

(or have not been discussed as related problems previously); directionality refers

to the direction in which a certain feature spreads, while Sour Grapes is a

question of whether harmony takes place when there is a blocker. However, I

suggest that these two issues are actually related because, as (6) shows, if it is

possible to achieve the attested leftward directionality, then the Sour Grapes

problem is also resolved. Notice that (6a) exhibits not only the attested

directionality but also more complete [-ATR] harmony, since the medial mid

vowel participates in the harmony triggered by the word-final [-ATR] vowel.

Hence, I suggest that once directionality is specified in the spreading

constraint itself, these two issues can be resolved at the same time. In order to

implement this proposal, I suggest the following two revised Spread constraints.

(7) Spread [F]-Left (Spread [F]-L) (Sasa 2006) If a feature [F] is associated with a vowel, the same feature [F] is associated with all the vowels to the left.

(7) enforces leftward spreading of a feature, without requiring rightward

spreading of the same feature. Likewise, (8) requires a feature to spread

rightward, but without (necessarily) forcing leftward spreading.

(8) Spread [F]-Right (Spread [F]-R) If a feature [F] is associated with a vowel, the same feature [F] is associated with all the vowels to the right.

Figure 11 shows some of the satisfaction and violation patterns of Spread

[F], Spread [F]-L, and Spread [F]-R; all of these spreading constraints are

! 119!

markedness constraints, and they evaluate candidates when a targeted feature

[F] is associated with a vowel in the output. (In other words, input

representations do not make any difference in the evaluation by the spreading

constraints.)

Spread [F] Spread [F]-L Spread [F]-R a) V1 V2 V3

Satisfied Satisfied Satisfied

b) V1 V2 V3

* Satisfied *

c) V1 V2 V3

* * Satisfied

Figure 11. Satisfaction and Violation of Spread 1 The configuration in (a) in Figure 11 satisfies Spread [F], Spread [F]-L, and Spread

[F]-R. In this configuration, all the vowels share the same feature [F] (or the same

feature [F] is linked to all the vowels). (b) violates both Spread and Spread [F]-R;

in (b), the feature [F] is not linked to the vowel, V3, and since Spread [F] requires

that a feature is linked to all the vowels, (b) incurs one violation of this constraint.

(b) also violates Spread [F]-R; there is a feature associated with V2 in this form,

and this feature is not linked to V3, which is to the right of V2. Thus, (b) violates

Spread [F]-R for V3. Spread [F]-L, on the other hand, is satisfied in (b); the feature

[F] associated with V2 is also associated with V1, and there is no preceding vowel

! 120!

for V1. Thus, Spread [F]-L is completely satisfied by (b). (c) violates both Spread

and Spread [F]-L but satisfies Spread [F]-R; the feature [F] associated with V2 is

also associated with the following vowel V3.

Figure 12 shows additional satisfaction and violation patterns of these

three spreading constraints.

Spread [F] Spread [F]-L Spread [F]-R a) V1 V2 V3 .!!!!!/01!

** Satisfied **

b) V1 V2 V3 .!!!!!!!!!!!!!!!!!!!!!!!!!/01!

** ** Satisfied

c) V1 V2 V3 [F]

Figure 12. Satisfaction and Violation of Spread 2 (a) in Figure 12 incurs two violations for Spread and Spread [F]-R since the

feature [F] associated with V1 is not linked to two vowel which are to the right of

V1. However, this configuration satisfies Spread [F]-L since there are no vowels

to the left of V1. (b) is the mirror image of (a), violating both Spread and Spread

[F]-L twice. However, Spread [F]-R is satisfied by this configuration because

there is no vowel to the right of V3 which [F] could spread to. Finally, an

interesting case is (c), a transparency case; this configuration satisfies none of the

family of the spreading constraints. Spread [F] is violated, since [F] skips or fails

! 121!

to be linked to the medial vowel. Spread [F]-L is violated because the feature

associated with V3 is not linked to V2, which is to the left of V3. Likewise, Spread

[F]-R is violated, too, since [F] is associated with V1 but the same [F] is not

associated with V2, which is to the right of V1.

In the next section, I demonstrate how the spreading constraint with

specified directionality accounts for the Pulaar data which Span Theory failed to

account for. More specifically, I show that the analysis with Spread [ATR]-L

resolves two problems in Pulaar, namely, the directionality problem and the

Sour Grapes problem.

4.2.2 The Analysis with Spread-Left

This section presents the full analysis of Pulaar with the harmony

constraint proposed in (7). In the analysis, I assume that the feature [ATR] is

binary, that is, I assume that both [+ATR] and [-ATR] are active, but this

assumption is explored fully in Section 4.4.

The harmony constraint in (9) enforces harmony.

(9) Spread [ATR]-Left (Spread [ATR]-L) (Sasa 2006) If a feature [ATR] is associated with a vowel, the same feature [ATR] is associated with all the vowels to the left.

Since I assume that ATR is binary in this section, in (9), the notation [ATR] refers

to both [+ATR] and [-ATR].

Second, the following faithfulness constraints are assumed.

! 122!

(10) a. Ident I-O [ATR] Word-Final (Id [ATR] (Fin)) (Petrova et al. 2000, 2006: 17; Kr23'4 2001; Walker 2001)

b. Ident I-O [ATR] (root) (Id (root) [ATR]) (cf. Beckman 1997, 1998)

Correspondent input and output segments in the root have the same specification for the feature [ATR].

c. Ident [ATR] (Id [ATR]) (cf. McCarthy and Prince 1995)

Correspondent input and output segments have the same specification for the feature [ATR].

In Pulaar, the vowel in the final syllable of a word either triggers harmony or

resists harmony. The positional faithfulness constraint in (10a) captures this

generalization; it functions to preserve input-output identity with regard to the

[ATR] specification of the word-final vowel.

In Pulaar, there are no [+high, -ATR] vowels and no [+low, +ATR] vowels.

The markedness constraints in (11) and (12) prohibit the occurrence of the

unattested vowels; (11) prohibits [+high, -ATR] vowels.

(11) No [+High, -ATR] (*ˆ/¨) (Archangeli and Pulleyblank 1994, Bakovic 2000, Kra‹mer 2001) High [-ATR] vowels are prohibited. (12) prohibits [+low, +ATR] vowels. (12) No [+Low, +ATR] (*æ) (Archangeli and Pulleyblank 1994, Bakovic 2000, Kra‹mer 2001) Low [+ATR] vowels are prohibited. As seen in Chapter 3, these two markedness constraints are highly ranked in

Pulaar to prohibit the occurrence of unattested vowels. I assume that the two

markedness constraints in (11) and (12) are also undominated in the analysis; any

! 123!

candidate containing unattested vowels loses to other candidates due to these

markedness constraints.

It also needs to be noted that the faithfulness constraints with regard to

vowel height, that is, Ident I-O [hi] (“input-output correspondents are identical

with regard to the feature [high]”) and Ident I-O [low] (“input-output

correspondents are identical with regard to the feature [low]”) are undominated

in Pulaar. As pointed out in Chapter 3, changing vowel height is not an attested

pattern to achieve a (more) harmonic form in Pulaar. That is, vowel lowering, as

observed in *[h´l-´r-d´] from an input /h´l-ir-d´/ is not an attested pattern.

Likewise, vowel raising, as in *[bo…te…ri] from the input /bo…ta…ri/, is not attested,

either. I assume that the undominated faithfulness constraints for vowel height

(Ident I-O [hi] and Ident I-O [low]) exclude candidates in which vowel lowering

or raising is observed.

The analysis of total harmony is presented in the tableau in (13).

(13) /søf-ru/_ [sof-ru] (basic total leftward harmony) /søf-ru/!!

*ˆ/*¨ Id [ATR] (fin)

Spread [ATR]-L

Id (root) [ATR]

Id [ATR]

!56!sof-ru! * * 76!søf-ru! *! 86!søf-r¨! *(!) *(!) * !In (13), candidate (13c) loses because of either the markedness constraint or the

positional faithfulness constraint for the final vowel. In this candidate, the word-

final vowel changes its ATR specification and surfaces as a [-ATR] high vowel,

which is not observed in this language. (13b) loses because of the directional

! 124!

spreading constraint. In (13b), the word-final vowel is specified as [+ATR] but its

[+ATR] feature is not linked to the vowel in the root (which is located to the left

of the word-final vowel). As a result, (13b) loses to (13a), which satisfies the

spreading constraint.1

(14) shows the analysis for the case where there is a mid vowel (which can

change its ATR specification) in the word-medial position.

(14) Interaction of Word-Final Faith and Spread [ATR]-L ,binnd-o…-wø/_ [binnd-ø…-wø] /binnd-o…-wø/ *ˆ/*¨! Id [ATR]

(fin) Spread [ATR]-L

Id (root) [ATR]

Id [ATR]

!!56!binnd-ø…-wø (Partial Left)!

! ! !!!!!!9! ! !!!!!!!!9!

b) binnd-o:-wø

(Partial Right)

!!!!!!!! !!!!!!!!!!!!! !!!!!99:! ! !!!!!!!!!

86!7(;;<=%>=&%!?@%$5A!B()*$6!

! !!!!!!!!!9:! ! ! !!!!!!!!9!

d) bˆnnd-ø…-wø (Total Left)!

9:! ! ! !!!!!!!!!!9! !!!!!!!!99!

!In (14), candidate (14d) loses because of the markedness constraint against high

[-ATR] vowels, and (14c) loses because of the word-final faithfulness constraint.

The two remaining candidates in (14), that is, (14a), the actual form, and (14b)

with unattested rightward directionality, are evaluated under Spread [ATR]-L.

The representations in Figure 13 show the configurations of these two

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 (13) does not show the ranking *ˆ/¨ >> Ident [ATR] (fin), but this ranking must

be established; for example, in (13), there is a possible input (because of Richness of the Base) /søf-r¨/, which surfaces as [sof-ru]. However, if the ranking is reversed, and Ident [ATR] (fin) dominates the markedness constraint, an unattested form *[søf-r¨] will win. Thus, throughout this section, I assume the ranking i) *ˆ/¨ >> Ident [ATR] (fin), and ii) *æ >> Ident [ATR] (fin).

! 125!

candidates; (14a) violates Spread [ATR]-L once; in this candidate, the [-ATR]

feature associated with the final vowel is linked to the medial mid vowel but not

to the initial vowel in the root. Thus, this candidate incurs one violation for

Spread [ATR]-L for the initial vowel (the vowel in the root) for not sharing the

same [-ATR] feature. (14b), on the other hand, violates this spreading constraint

twice; as in (14a), there is a [-ATR] feature associated with the final vowel.

However, this [-ATR] feature is not linked to both the medial mid vowel and the

high vowel in the root. As a result, (14a) satisfies Spread [ATR]-L better than

(14b), and is selected as optimal in (14). Notice that non-directional Spread fails to

resolve the tie in the word-medial mid vowel case, as illustrated in Chapter 3.

14a) 14b) i ø… ø i o… ø [+ATR] [-ATR] [+ATR] [-ATR] Spread [ATR]-L: * ([-ATR] not linked to [i]) ** ([-ATR] not linked to [i] /[o]) (violated once) (violated twice) Figure 13. Configurations of (14a) and (14b) (14) also shows that the Sour Grapes problem is solved by assuming the

directional spreading constraint. The following analysis in (15) confirms this

suggestion; in (15), the spreading constraint not only correctly predicts the

attested directionality, but also avoids Sour Grapes.

! 126!

(15) [barø…-di]_[baro…-di]: harmony with a blocker, no Sour Grapes /barø…-di/ *æ Id [ATR]

Id (Root) [ATR]

Id [ATR]

!a) b a r o… d i !!!!!!!!!!!.!!!!!!!!!!!!!.! [-ATR] [+ATR]

b) b a r ø… d i .!!!!!!!!!!!!.! [-ATR] [+ATR]

c) b æ r o… d i ! [+ATR]

In (15), the low vowel in the root [a] is a blocker of the harmony since this vowel

cannot change its ATR specification. (15c) loses because of the markedness

constraint prohibiting [+low, +ATR] vowels. As seen in the analysis in (9) in

Chapter 3, the non-directional spreading constraint will fail to discriminate

between (15a) and (15b), and as a result, the Sour Grapes problem arises. As seen

in (15), however, this problem can be avoided by enforcing leftward harmony

by specifying directionality in the harmony/spreading constraint.

Given (14) and (15), I suggest that directionality and the Sour Grapes

problems are related. Even though these problems appear to be independent of

each other, as (14) and (15) show, if an analysis correctly predicts the attested

directionality, the Sour Grapes problem is also resolved. I suggest that specifying

the directionality is the key to the solution to both of these issues because the

spreading constraint with specified directionality correctly predicts the attested

directionality and as a result, enforces more complete harmony.

! 127!

The following two tableaux show two more cases observed in Pulaar;

first, (16) is the analysis of another Sour Grapes case. This confirms the claims

made above. Second, (17) is the analysis of another directionality case in which

there is a trigger in the word medial position.

(16) [barø…-gel]_[baro…-gel]: harmony with a blocker, no Sour Grapes /barø…-gel/ *æ Id [ATR] (fin) Spread

[ATR]-L Id (Root)

[ATR] Id

!a) b a r o… -gel * * b) b a r ø… -gel **! c) b a r ø… -g´l *! * d) bæro…-gel *! * **

Candidate (16c) loses because of the positional faithfulness constraint for the

vowel in the final syllable, and (16d) is excluded by the markedness constraint

against a [+low, +ATR] vowel. The actual surface form in (16a) is selected over its

competitor (16b) by the spreading constraint. Thus, the Sour Grapes case in (16)

is resolved by the same mechanism observed in (15).

(17) shows another case of leftward directionality. In (17), there is a trigger

word-medially, and the trigger affects the ATR specification of the preceding

vowel, but not of the following vowel. (17b) loses because of the word-final

faithfulness constraint and (17c) loses because of the markedness constraint. The

remaining two candidates, (17a) and (17d), are evaluated under Spread [ATR]-L,

and this constraint prefers (17a), the actual form; (17a) violates the spreading

constraint twice because the [-ATR] feature associated with the word-final vowel

is not linked to two vowels. (17d) incurs three violations of the spreading

! 128!

constraint; the [-ATR] feature of the final vowel is not associated with two

preceding vowels and the [+ATR] feature of the word-medial vowel is not

associated with the preceding vowel (one additional violation). As a result,

Spread [ATR]-L prefers (17a) to (17d).2

(17)!/h´l-ir-d´/_[hel-ir-d´] (word-medial trigger case) /h´l-ir-d´/ *ˆ/*¨! Id [ATR]

Id (root) [ATR]

Id [ATR]

!a) hel-ir-d´ !" [+ATR] [-ATR]

b) h´l-ir-de !"[-ATR] [+ATR]

c) h´l-ˆr-d´ [-ATR]

! ! ! !

d) h´l-ir-d´ """""""!"""!"""""!" [-] [+] [-]

Thus far, I have demonstrated that the directional spreading constraint

correctly predicts the attested leftward directionality. (18) shows that the same

mechanism also correctly predicts the opaque behavior of the low vowel.

(18) Low Vowel Opacity /bo…t-a…-ri/ *æ Id [ATR]

Id (root) Id [ATR]

!a) bø…t-a…-ri ** * * b) bo…t-a…-ri ***! c) bo…t-æ…-ri *! * d) bø…t-a…-rˆ *! * **

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C!In (17), I use the notation [+] to indicate a [+ATR] feature and [-] for [-ATR] in candidate (17c) due to space limitations.

! 129!

Candidate (18c) loses because of the markedness constraint against a [+low,

+ATR] vowel, and (18d) loses because of the word-final faithfulness constraint

(or because of *ˆ/¨, which is not included in (18) because of space limitations).

(18a) satisfies Spread [ATR]-L better than (18b); in (18a), the two [-ATR] vowels

do not share the same [+ATR] specification associated with the word-final vowel

and thus, this candidate incurs two violations. (18b) incurs three violations of this

constraint because the [+ATR] feature of the word-final vowel is not shared by

two of the preceding vowels (two violations) and the [-ATR] specification is not

linked to the preceding mid [+ATR] vowel (one violation). As a result, Spread

[ATR]-L prefers the actual form in (18a) to its competitor (18b).

There is one note to be added to the analysis in (17) and (18). I assumed

that in (17d), *[h´l-ir-d´], there are two independent [-ATR] features associated

with two [-ATR] vowels. Likewise, I assumed that there are two separate [+ATR]

features that are independently associated with two [+ATR] vowels in (18b),

*[bo…ta…ri]. However, another possible representation for these candidates is a

gapped configuration, where the same [-ATR] feature (in (17)) or the same

[+ATR] feature (in (18)), is associated both with the final vowel and with the

initial vowel, skipping the medial vowel. Since the feature skips the medial

vowel, this vowel surfaces as a ‘default’ vowel, as designated by the markedness

constraints: in (17), as a [+ATR] vowel and in (18), as a [-ATR] vowel.

! 130!

Such candidates actually violate or satisfy the spreading constraint equally

as well as does the actual form, since in a gapped configuration, the feature is not

linked to only one vowel, as in the actual candidates (17a) and (18b). However,

since there are no reasons in Pulaar to assume gapped configurations, the

markedness constraint prohibiting such configurations, namely No Gap in (7) in

chapter 1, is assumed to be undominated in this language.

The ranking lattice for Pulaar ATR harmony is presented in Figure 14.

*ˆ/¨, *æ !

Ident [ATR] (fin) !" Spread [ATR]-L

Ident (root) Ident [ATR] Figure 14. Ranking Lattice: Pulaar/Spread

In Pulaar, the ranking Ident [ATR] (word final) >> Spread [ATR]-L is crucially

established to correctly predict the attested directionality. As seen in (14), the

word-final faithfulness constraint excludes the candidate (14c) that exhibits

unattested directionality; (14) shows that if this positional faithfulness constraint

were dominated by the spreading constraint, then (14c) would be selected over

the attested form in (14a). (14) also shows that the positional faithfulness

constraint alone is not sufficient to predict the attested directionality; two

! 131!

candidates (14a: partial leftward) and (14b: partial rightward) tie under the

positional faithfulness constraint; the directional spreading constraint functions as

a tie-breaker. Thus, the analysis in (14) suggests that directionality effects cannot

simply be attributed to positional faithfulness; to reiterate, when two candidates

with different spreading directionalities satisfy the positional faithfulness

constraint, it is the directional spreading (or harmony) constraint that breaks the

tie between such candidates.

(14), along with (15), also suggests that specifying directionality solves the

Sour Grapes problem, which the original non-directional spreading constraint

fails to resolve. As (14) and (15) show, two problems, which appear to be

independent of each other, are, in fact, related; specifying directionality in the

spreading constraint is the single key to solving both problems.

The analyses presented in this section, hence, suggest that Spread

successfully avoids the problems that the data from Pulaar presents, even

though the original proposal needs some modifications, as discussed in Section

4.2.1. In the next section, Section 4.3, I present a different approach to Pulaar

harmony, namely, an ABC approach, and investigate how ABC accounts for the

directionality problem observed in Pulaar.

4.3 The ABC Analysis

As stated in Chapter 2, the key assumption of ABC (Agreement-By-

Correspondence) is that segments that are similar correspond (Rose and Walker

2004, Walker 2009). The ABC analysis was originally proposed for consonant

! 132!

harmony, or more accurately, long-distance consonant agreement with

intervening segments, but Walker (2009), for example, presents an analysis for

the ATR harmony observed in Menominee, assuming that the feature ATR is

binary. In this section, I present the ABC analysis of Pulaar assuming binary ATR

so that the ABC analysis can be compared with the spreading analysis on the

same grounds. However, I will reconsider the issue of binary ATR in Section 4.4

of this chapter.

To implement one of the ABC assumptions that similar segments

correspond in Pulaar, I propose the following output correspondence

constraints; (19) states that [-high] vowels, that is, mid vowels and low vowels,

correspond.

(19) Corr [-Hi]-[-Hi] (Corr [-hi]) (cf. Walker 2009) Let S be an output string of segments and let X and Y be [-consonantal,

-high] segments. If X and Y belong to S, then X and Y correspond. (20) states that high and mid vowels are in correspondence.

(20) Corr [-Lo]-[-Lo] (Corr [-lo]) (cf. Walker 2009) Let S be an output string of segments, and let X and Y be [-consonantal,

-low] segments. If X and Y belong to S, then X and Y correspond. I suggest that the key similarity feature in Pulaar ATR harmony is vowel height,

rather than, say, backness; for example, non-low vowels agree in the [+ATR]

feature, or in ABC terms, are identical in the [+ATR] feature, if the trigger is

[+ATR]. Likewise, if a trigger is [+low, -ATR], non-high vowels are identical in

the [-ATR] feature. Thus, I propose that it is reasonable to group vowels with

regard to the similarity in height, rather than other vowel features. In addition to

! 133!

the height-specific correspondence constraints as in (19) and (20), the general

correspondence constraint for vowels of any height is also assumed to be

operative in the grammar. The correspondence constraint in (21) requires that

vowels of any height be in correspondence.

(21) Corr V-V (Corr V-V) (cf. Walker 2009) Let S be an output string of segments and let X and Y be [-consonantal] segments. If X and Y belong to S, then X and Y correspond.

In ABC, the fact that segments are in correspondence does not mean that

they are identical with respect to a certain feature. In other words, even if two

vowels are in correspondence, that does not mean that these two vowels are

necessarily identical in their ATR specifications. The correspondence identity

constraints, such as in (24), require that the segments in correspondence be

identical with regard to a certain feature.

(22) Ident VV [ATR] (Id VV [ATR]) (Walker 2009) Let X be a segment in the output and Y be a correspondent of X in the output;

i) if X is [+ATR], then Y is [+ATR] ii) if X is [-ATR], then Y is [-ATR]. (22) states that if two (or more) vowels are in correspondence, these vowels are

identical in [ATR] specification.

In addition to (19) through (22), the following constraints are also

necessary to account for the Pulaar data.

(23) a. Ident I-O [ATR] Word-Final (Id [ATR] (Fin)) (Petrova et al. 2000, 2006: 17; Kr23'4 2001; Walker 2001)

! 134!

b. Ident [ATR] (Id [ATR]) (cf. McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [ATR].

c. No [+High, -ATR] (*ˆ/¨) (Archangeli and Pulleyblank 1994, Bakovic

2000, Kra‹mer 2001) High [-ATR] vowels are prohibited.

d. No [+Low, +ATR] (*æ) (Archangeli and Pulleyblank 1994, Bakovic 2000, Kra‹mer 2001)

Low [+ATR] vowels are prohibited.

As in the analysis with Spread, it is necessary to maintain the identity of the

trigger of the harmony. (23a) functions to preserve the input specification of the

word-final vowel, which is the trigger of harmony. In addition to the faithfulness

constraints in (23b) and (23c), the markedness constraints prohibiting the

unattested segments are also necessary to predict the actual forms. In addition to

the constraints listed in (23), I assume that the faithfulness constraints Ident

[hi]/Ident [low] (that militate against any change in the height specification) are

undominated; any candidates in which vowels change their height specifications

are excluded by these height faithfulness constraints.3

The ABC analysis of the basic ATR harmony pattern is presented in

tableau (24). In the following tableaux, I use subscripts to indicate

correspondence.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3 In the feature linking analysis, I assumed that another markedness constraint,

No Gap, is also undominated in Pulaar. In the ABC account, a different approach is taken to prohibit gapped configurations. The ABC solution to gapped configurations is presented in (31) of this section.

! 135!

(24) Basic harmony /s´r-du/ *ˆ/¨ Id

(Fin) Id VV [ATR]

Corr [-hi]

Corr [-lo]

Corr V-V

Id [ATR]

!sexr-dux * b) s´r-du *! * c) s´xr-dux *! d) s´xr-d¨x *(!) *(!) *

In (24a), both of the vowels are in correspondence and they are identical in their

[+ATR] features. (24b) is a fully faithful candidate, in which neither one of the

vowels is in correspondence. In (24c), both vowels are in correspondence but

they are not identical in ATR, and in (24d), both of the vowels are in

correspondence, as in (24a), but they are both [-ATR].

In (24), candidate (24d) loses either because of the markedness constraint

or because of the word-final faithfulness constraint. (24b) loses because two non-

low vowels in the output do not correspond, that is, this candidate violates Corr

[-Lo]. Candidate (24c) loses because of Ident V-V [ATR] since the two vowels in

correspondence are not identical in their [ATR] specifications. (24) shows the

ranking Corr [-lo], Ident VV [ATR] >> Ident I-O [ATR]. This ranking is the

ranking for harmony languages, as pointed out in Walker (2009) (cf. Figure 5 in

Chapter 1).

The tableau in (25) gives the analysis for partial harmony. In (25), there is

a mid vowel word-medially, and this mid vowel is identical to the following mid

vowel in the last syllable. However, the high vowel in the first syllable remains

[+ATR]. Thus, the directionality effect is observed in this case.

! 136!

(25) Partial harmony/leftward directionality 1 ([+high] vowel as a blocker) /binndo…wø/_ [binndø…wø] /i-o-ø/ *ˆ/¨ Id

(Fin) Id VV [ATR]

Corr [-hi]

Corr [-lo]

Corr V-V

Id I-O [ATR]

!a) i-øx-øx * * * b) ix-ox-ø *! * * c) ˆx-øx-øx *! * d) ix-ox-ox *! * In (25), (25c) loses because of the markedness constraint, and (25d) loses because

of the positional faithfulness constraint for the final vowel. Corr [-hi] prefers

(25a) to (25b); in (25a), two [-high] vowels are in correspondence while in (25b),

the medial vowel corresponds to the preceding high [+ATR] vowel but does not

correspond to the following mid vowel. As a result, the correspondence

constraint for non-high vowels prefers (25a) to (25b). (25) shows the ranking

*ˆ/¨, Ident (Fin) >> Corr [-lo], Corr V-V.

(25) shows that in ABC, the directionality of harmony can be accounted

for by lack of correspondence. Candidates (25a) and (25b) exhibit different

directionalities (in (25a), the attested leftward and in (25b), unattested rightward).

The difference in directionality is captured by the different correspondence

relationships in these two candidates; in (25a), leftward directionality is attributed

to the fact that the initial high [ATR] vowel is not in correspondence, and in (25b),

rightward directionality is attributed to the fact the word-final mid non-ATR is

not in correspondence. As seen in (25), the output correspondence constraint,

Corr [-hi], favors the candidate in which both of the mid vowels are in

correspondence. Thus, on the basis of the observation in (25), I propose DLC,

! 137!

namely, ‘Directionality by Lack of Correspondence,’ and suggest that

directionality effects are accounted for through DLC in the ABC approach.4

Now, let us consider another issue in Pulaar, namely, Sour Grapes. (26)

shows the analysis of the Sour Grapes case.

(26) Sour Grapes resolved: /barø-gel/ _ [baro-gel] /a-ø-e/ Id

(Fin) Id VV [ATR]

Corr [-hi]

Corr [-lo]

Corr V-V Id [ATR]

!a) a-ox-ex * * * b) ax-øx-e * *! * c) a-øx-ex *! ** d) ax-øx-´x *! * In (26), the actual surface form is (26a), and (26b) is the Sour Grapes competitor.

Candidate (26d) loses because of the positional faithfulness constraint.

Candidate (26c) is excluded by the Ident VV [ATR] constraint, since the vowels in

correspondence are not identical with respect to [ATR] specification in this

candidate. The remaining two candidates equally violate the correspondence

constraints for non-high vowels; in (26a), the low vowel [a] is not in

correspondence with the other non-high vowels and in (26b), the final mid vowel

[e] does not correspond with other non-high vowels. The competition goes to

the next correspondence constraint, Corr [-Lo], which prefers the actual form; in

(26a), two non-low vowels are in correspondence, while in (26b), one of the non-

low vowels, the final [e], does not correspond with the other non-low vowel. As

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4 One might ask, however, what if all the vowels are in correspondence; more

specifically, what result will be obtained in (25), if an additional candidate, [ix-øx-øx], is considered. The answer to this question is addressed in (28) of this section.

! 138!

a result, the actual form is successfully selected as optimal. (26) shows the

ranking *æ, Ident (Fin) >> Corr [-hi].

Both in (25) and in (26), the winner is the candidate that contains a vowel

that is not in correspondence with the other vowels in a word. I suggested that

the ranking Ident VV [ATR] >> Corr [-lo] must be established. This ranking

predicts the attested form, as seen in (27); in (27), all of the vowels are in

correspondence in each candidate except in candidate (27a).

(27) Partial harmony/leftward directionality 2 ([+high] vowel as a blocker) /binndo…wø/_ [binndø…wø] /i-o-ø/ *ˆ/¨ Id

(Fin) Id VV [ATR]

Corr [-hi]

Corr [-lo]

Corr V-V

Id [ATR]

!a) i-øx-øx * * * b) ix-ox-øx *! c) ix-øx-øx *! * d) ix-ox-ox *! * The realization of candidate (27c) is the same as that of (27a); the difference

between these candidates is that in (27a), the final vowel is not in correspondence

with the other vowels while in (27c), all of the vowels are in correspondence. In

(27), the positional faithfulness constraint for the word-final vowel excludes

candidate (27d). The correspondence identity constraint with regard to [ATR]

excludes (27b) and (27c). As a result, candidate (27a) is selected as optimal even

though one of the vowels in this candidate is not in correspondence.

However, one might raise a question with regard to the ranking

established in (27); that is, why should (27a) be the winner, rather than (27c)? As

mentioned, the realization of these candidates is the same, and in both of the

! 139!

candidates, the attested directionality is observed. To investigate this question, let

us reverse the ranking established in (25), and assume that the Ident VV [ATR]

constraint is dominated by the output correspondence constraints. This is

illustrated in the tableau in (28). In (28), the reverse ranking is assumed so that

(28c) would be selected over (28a) (see (27); the ranking Ident VV [ATR] >> Corr

[-hi], Corr V-V selects (27a) over (27c)).

(28) Reverse ranking fails: /binndo…wø/_ [binndø…wø] /i-o-ø/ *ˆ/¨ Id

(Fin) Corr [-hi]

Corr [-lo]

Corr V-V Id VV [ATR]

Id [ATR]

!a) i-øx-øx *(!) *(!) * "b) ix-ox-øx * !c) ix-øx-øx * *! In (28), the winner should be either (28a) or (28c). Because of the ranking Corr

[-Lo], Corr V-V >> Ident VV [ATR], (28a) loses, but (28c) is still in the

competition. However, the problem with this ranking is that, if the remaining

candidates are (28b) with rightward directionality and (28c) with leftward

directionality, Ident VV [ATR] fails to discriminate between these two candidates.

As pointed out in Rose and Walker (2004) and Walker (2009), the Ident VV [ATR]

constraint performs a pair-wise comparison; (28c) incurs one violation of this

faithfulness constraint for the [ox...øx] pair. Likewise, (28b) also incurs one

violation of this constraint for the [ix...øx] pair. Thus, these two candidates equally

violate the Ident VV [ATR] constraint. As a result, the competition goes to the

general faithfulness constraint, and Ident I-O [ATR] prefers (28b).

! 140!

The same problem is observed in (29). In (29), the same case as in (26) is

examined, but with the ranking assumed in (28).

(29) Sour Grapes: /barø-gel/ _ [baro-gel] /a-ø-e/ Id

(Fin) Corr [-hi]

Corr [-lo]

Corr V-V Id V-V [ATR]

Id [ATR]

a) a-ox-ex *(!) *(!) * "b) ax-øx-eX * !c) ax-ox-ex * *! In (29), candidate (29a) loses because of the correspondence constraints, but (29c)

is still in the competition. (29c) and (29b), both of which satisfy the

correspondence constraints, tie under the output correspondence faithfulness

constraint. As in (21), the general faithfulness constraint is the tie-breaker in (29),

and as a result, (29b) is wrongly selected as the winner. The cases in (28) and (29)

show that if all of the vowels are in correspondence, Ident VV [ATR] fails to

resolve the tie; that is, the directionality effects (which are related to Sour Grapes,

as seen in (29)) cannot be attributed to output correspondent faithfulness.

I argue, therefore, that the ranking in (26), Ident VV [ATR] >> Corr [-lo],

Corr V-V, must be established to avoid this problem. If all of the vowels are in

correspondence, the faithfulness constraint for the output correspondents fails to

prefer the candidate with the attested directionality of harmony. This suggests

that in ABC, directionality is achieved, or more specifically, the unattested

directionality is blocked (as seen in (26b)), by the lack of correspondence

between the preceding high vowel and the following mid vowel. Thus, I propose

! 141!

that in ABC, directionality is achieved or unattested directionality is blocked by

DLC, Directionality by Lack of Correspondence.

The analysis in (26) (in which the case of/barø-gel/_[baro-gel] was

considered) shows that establishing correspondence between non-high vowels is

the key to the solution to the Sour Grapes problem. (30) shows, however, that

establishing a correspondence relationship between non-high vowels predicts an

unattested pattern.

(30) Problematic correspondence: /h´l-ir-d´/_[hel-ir-d´] /´-i-´/ Id

(Fin) Id VV [ATR]

Corr [-hi]

Corr [-lo]

Corr V-V Id [ATR]

!a) ex-ix-´ *(!) *(!) * * "b) ´x-i-´x * * c) ex-ix-´x *! * d) ex-ix-ex *! ** In (30), (30c) and (30d) are excluded from the competition because of the Ident

VV [ATR] constraint and the word-final faithfulness constraint, respectively.

Between the remaining candidates, Corr [-hi] prefers (30b), where two non-

adjacent mid vowels are identical in their ATR specification. In (30a), the actual

form, on the other hand, the medial high vowel and the preceding mid vowel

are in correspondence but the final mid vowel is not in correspondence at all. As

a result, (30a) violates Corr [-hi]. (26) shows that the key to the solution to Sour

Grapes is to establish correspondence. In (30), on the other hand, this key

assumption predicts an unattested harmony pattern by establishing an

unwanted correspondence.

! 142!

In laying out the typology of nasal agreement, Rose and Walker (2004)

point out that proximity plays another important role. For example, in two

languages with nasal agreement, Kikongo and Ndonga, nasal agreement fails in

Ndonga if the consonants are not in adjacent syllables, while in Kikongo, nasal

agreement is observed even if the segments are not in adjacent syllables (Rose

and Walker 2004: 494). To differentiate these two types, Rose and Walker (2004)

suggests the locality constraint as in (31).

(31) Proximity (Prox) (Rose and Walker 2004: 494) Correspondent segments are located in adjacent syllables. I suggest (31) as a solution to the problem in (30); in Pulaar, since there are no

reasons to assume a gapped configuration, I assume that (31) is an undominated

constraint in the grammar. The solution with (31) is presented in (32).

(32) Locality in correspondence: /h´l-ir-d´/_[hel-ir-d´] /´-i-´/ Prox Corr

[-hi] Corr [-lo]

Id VV [ATR]

Corr V-V Id [ATR]

#a) ex-ix-´ * * * * b) ´x-i-´x *! * * (32b) violates Proximity because the two segments in correspondence are not

adjacent. (There is an intervening vowel which does not correspond to either

flanking vowel.) (32a), on the other hand, satisfies this markedness constraint

because the two vowels in correspondence are adjacent; there are no intervening

segments between the two vowels in correspondence. As mentioned, the

Proximity constraint is assumed to be high-ranked in this language, and in fact,

(32) shows the ranking Proximity >> Corr [-hi].

! 143!

Finally, (33) presents the solution to the opacity case. (33) shows that the

solution to opacity is similar to the solution presented in (32); Prox excludes the

candidate in (33d) in which vowels in correspondence are not adjacent.

(33) Opacity: /bo…ta…ri/_[bø…ta…ri] /o-a-i/ Id

(Fin) Prox Id VV

[ATR] Corr [-hi]

Corr [-lo]

Corr V-V

Id [ATR]

!a) øx-ax-i * * * b) o-a-i *(!)* **(!) **(!)* c) ox-ax-ix *!* d) ox-a-ix *! * * In (33), candidate (33d) is ruled out because of the proximity constraint, and (33c)

is excluded by the output correspondent faithfulness constraint. Candidate (33b),

where none of the vowels is in correspondence, is ruled out by either one of the

output correspondence constraints. (33) shows the ranking Prox >> Corr [-lo].

Figure 15 presents the summary of the ranking arguments.

Prox *æ, *ˆ/¨ Ident (fin) !" Ident VV [ATR] .!

Corr [-hi], Corr [-lo], Corr V-V! .!

Ident I-O [ATR] Figure 15. Ranking Lattice: Pulaar/ABC

! 144!

I assume that the ranking *ˆ/¨, *æ >> Ident (fin) must be established in the ABC

analysis as well; if these markedness constraints do not dominate the word-final

faithfulness constraint, candidates with an unattested vowel (such as [+high, -

ATR] vowels) will be selected as a winner.

In ABC, the directionality of harmony is explained through lack of

correspondence. As demonstrated, the Ident VV [ATR] constraint cannot resolve

the tie between two candidates with different directionalities of harmony.

Rather, directionality is attributed to the fact that there is a vowel in a candidate

that is not in correspondence; the correspondence constraints, then, select the

candidate that exhibits the attested directionality. As stated above, the

directionality and Sour Grapes problems are related, and as seen in this section,

the Sour Grapes problem is resolved by the same mechanism. However, the

mechanism required for directionality and Sour Grapes over-generates

unattested patterns. That is, the system predicts some unwanted correspondence

relationships. To prohibit such unwanted results, I suggested a solution using

another ABC constraint, Proximity, so that the segments in correspondence are

located in adjacent syllables.

Thus far, I have demonstrated that both feature linking and ABC

successfully account for the attested data. The next section presents the

similarities and differences between these two approaches; in Section 4.4.1, I refer

to the role of positional faithfulness as observed in these approaches, and in

Section 4.4.2, I discuss the differences between these two approaches.

! 145!

4.4 General Discussion

4.4.1 Positional Faithfulness in Harmony

In Chapter 3, I mentioned that directionality effects cannot be simply

attributed to other phonological phenomena, such as positional faithfulness

(Beckman 1997, 1998). The preliminary analyses of Pulaar as presented in

Chapter 3 with non-directional Spread illustrate this point; positional faithfulness

by itself cannot resolve the tie between two candidates which exhibit different

spreading directionalities. To resolve this problem, in Section 4.2, I proposed an

analysis with the directional Spread [ATR]-L to correctly achieve the attested

directionality. The analysis showed, however, that this does not mean that

positional faithfulness is unnecessary to account for harmony; one might claim

that it is redundant to assume two mechanisms to achieve attested directionality:

specifying directionality in harmony (spreading) constraints and positional

faithfulness. As discussed in this chapter, however, such a claim is incorrect.

First, it needs to be made clear that the role of positional faithfulness, in

the larger context of OT phonology, is not limited to guaranteeing the input-

output identity of a harmony trigger. For example, positional faithfulness plays a

crucial role in accounting for positional asymmetries, say, in obstruent voicing;

for example, in a language where voiced obstruents are prohibited in word-final

position but they freely appear elsewhere, the ranking Ident (pre-sonorant)

[voice] >> *Voice >> Ident [voice] predicts that voiced obstruents are allowed in

pre-sonorant positions while they are prohibited elsewhere (cf. Petrova et al.

! 146!

2006). Therefore, positional faithfulness is independently motivated as part of the

OT grammar; it is true that positional faithfulness functions to preserve the

input-output identity of the trigger in harmony, but its role is not limited to this.

Second, even if a revision of the theory is introduced, positional

faithfulness is indispensable. This is illustrated in (34); the directionality example

as presented in (14) above is repeated.

(34) Interaction of Word-Final Faith and Spread [ATR]-L ,binnd-o…-wø/_ [binnd-ø…-wø] /binnd-o…-wø/ Ident [ATR]

Id (root) [ATR]

Id [ATR]

!!56!binnd-ø…-wø (Partial Left)!

! !!!!!!9! ! !!!!!!!!9!

b) binnd-o:-wø

(Partial Right)

!!!!!!!!!!!!! !!!!!99:! ! !!!!!!!!!

86!7(;;<=%>=&%!?@%$5A!B()*$6!

!!!!!!!!!9:! ! ! !!!!!!!!9!

!In (34), binary ATR is assumed. I suggested that in a case such as in (34), the

directional spreading constraint breaks the tie between (34a) and (34b). It is true

that these candidates both satisfy the positional faithfulness constraint for the

word-final vowel. However, if the word-final faithfulness constraint is not in the

tableau, neither (34a) nor (34b) wins. In fact, (34c), which exhibits an unattested

spreading directionality from the first vowel to the right, is selected as optimal.

The analysis repeated in (34) suggests that spreading constraints with

specified directionality and positional faithfulness constraints (such as Ident

[ATR] (Final)) complement each other to achieve the attested directionality. The

positional faithfulness constraint can exclude one of the candidates with

! 147!

unattested directionality. However, in some cases, as illustrated in (34), positional

faithfulness is silent. If positional faithfulness is silent, then the directional

spreading constraint breaks the tie. Thus, both positional faithfulness and the

harmony/spreading constraint with specified directionality function together to

achieve the attested directionality, or to block the unattested directionality.

The same is true with the ABC analysis. As mentioned, directionality is

correctly predicted, or more accurately, the unattested directionality is blocked,

by the DLC (Directionality by Lack of Correspondence) effect. As (35) shows,

however, DLC is not possible without the positional faithfulness constraint.

(35) Partial harmony ([+high] vowel as a blocker) (cf. (26)) /binndo…wø/_ [binndø…wø] /i-o-ø/ *ˆ/¨ Id

(Fin) Corr [-hi]

Corr [-Lo]

Id V-V [ATR]

Corr V-V

Id [ATR]

!a) i-øx-øx * * * b) ix-ox-ø *! * * c) ˆx-øx-øx *! * d) ix-ox-ox *! * As discussed, candidate (35a), the actual form, is achieved through the lack of

correspondence of the initial vowel [i]. As (35d) shows, this is achieved because

of the word-final faithfulness constraint prohibiting /ø/ from becoming [+ATR].

Without this positional faithfulness constraint, (35d) would win over (35a) since

(35d) satisfies both of the output correspondence constraints.

Therefore, obtaining attested directionality, or blocking unattested

directionality, is not achieved by the directional spreading constraint or by the

output correspondence constraint alone. These two approaches both require

! 148!

positional faithfulness; in the ABC analysis, positional faithfulness is crucial in

blocking correspondence, and in the analysis with directional Spread, the

directionality in the spreading constraint itself is not sufficient to block an

unattested directionality. Thus, both feature linking and ABC crucially rely on

positional faithfulness in predicting the attested directionality correctly.

4.4.2 Privative [ATR]

In sections 4.2 and 4.3, I presented the spreading and ABC analyses

assuming that the feature [ATR] is binary. The question addressed in this section,

then, is what if the feature [ATR] is privative? To investigate this question, first,

the analysis with Spread [ATR]-L is presented.

If privative ATR is assumed, that means that the active feature in

harmony is only ATR. In other words, [-ATR] is assumed to be inactive and

assumed not to spread. The spreading constraint in (36) is used to enforce

harmony under privative ATR. The analysis with (36) is presented in (37).

(36) Spread [ATR]-Left (Spread [ATR]-L) (cf. Sasa 2006) If a feature [ATR] is associated with a vowel, the same feature [ATR] is associated with all the vowels to the left.

(37) /søf-ru/ _ [sof-ru] (basic total leftward harmony) /søf-ru/!!

*ˆ/*¨ Id [ATR] (fin)

Spread [ATR]-L

Id (root) [ATR]

Id [ATR]

!56!sof-ru [ATR]!

76!søf-ru .! [ATR]

86!søf-r¨! *(!) *(!) *

! 149!

In (37a), there is an [ATR] feature associated with the final vowel and it is also

associated with the first vowel. In (37b), the [ATR] feature of the final vowel is

not associated with the vowel in the first syllable, and thus, it violates the

spreading constraint. In (37c), there are no [ATR] features and the spreading

constraint is vacuously satisfied. However, this candidate is ruled out either by

the undominated markedness constraint against [+high] non-ATR vowels, or by

the positional faithfulness constraint. (37) shows that Spread [ATR]-L successfully

enforces harmony in the correct direction, even with the assumption of privative

[ATR].

(38) shows that Sour Grapes is not a problem under the assumption of

privative ATR.

(38) [barø…-di]_[baro…-di]: Harmony with a blocker, no Sour Grapes /barø…-di/ Id [ATR]

Id (Root) [ATR]

Id [ATR]

!a) b a r o… d i !!!!!!!!!!!!!!!!!!!!!!!!!!!!.! [ATR]

b) b a r ø… d i !!!!!!!!!!!!!.! [ATR]

c) b a r ø… d ˆ *! * In (38), there is a low vowel blocker which cannot change to [ATR]. Still, the

analysis with privative ATR successfully avoids the Sour Grape candidate in

(38b). In (38a), the spreading of [ATR] is more complete than in (38b), and as a

result, Spread [ATR]-L still resolves the tie between (38a) and (38b).

! 150!

However, (39) shows that the analysis with Spread [ATR]-L fails to predict

leftward directionality. In (39), all the candidates satisfy Spread [ATR]-L; as

illustrated in Figures 11 and 12, Spread [ATR]-L is silent on rightward spreading.

(39) Leftward fails (cf. (14)): ,binnd-o…-wø/_ [binnd-ø…-wø] /binnd-o…-wø/ Id [ATR]

Id (root) [ATR]

Id [ATR]

!56!binnd-ø…-wø .! [ATR]

! !!!!!!! ! !!!!!!!!9!

" b) binnd-o:-wø

| [ATR]

!!!!!!!!!!!!! !!!!!! ! !!!!!!!!!

86!7(;;<=%>=&%!

! [ATR]

!!!!!!!!!9:! ! ! !!!!!!!!9!

d) bˆnnd-ø…-wø ! ! !!!!!!!!!!9! !!!!!!!!99!

The problem in (39) is that candidates (39a) and (39b) equally satisfy the

positional faithfulness constraint, the spreading constraint, and the root

faithfulness constraint. These candidates are evaluated by the general faithfulness

constraint for the ATR feature, and this faithfulness constraint prefers candidate

(39b). Thus, if ATR is assumed to be privative, the directional spreading

constraint is silent and as a result, it fails to resolve the tie between leftward (39a)

and rightward (39b).

It seems, however, that the problem in (39) can be resolved if privative

RTR (Retracted Tongue Root) is assumed, instead of privative ATR; that is,

suppose that we assume that Pulaar exhibits RTR, rather than ATR, harmony.

! 151!

The spreading constraint for RTR harmony is presented in (40). The analysis with

(40) is presented in (41).

(40) Spread [RTR]-Left (Spread [RTR]-L) If a feature [RTR] is associated with a vowel, the same feature [RTR] is associated with all the vowels to the left.

(41) Problem solved? (cf. (39)): ,binnd-o…-wø/_ [binnd-ø…-wø] /binnd-o…-wø/ *ˆ/*¨! Id [RTR]

(fin) Spread [RTR]-L

Id (root) [RTR]

Id [RTR]

#56!binnd-ø…-wø .! [RTR]

! !!!!!!!!9!

b) binnd-o:-wø

| [RTR]

! ! !99:!

! !!!!!!!!!

86!bˆnnd=ø>=&ø ! [RTR]

! ! ! !!!!!!!!9!

d) binnd-o…-wo ! 9:! ! !!!!!!!!!!9! !!!!!!!!99!

!In (41), all the constraints remain the same as in (39), except that the faithfulness

constraints evaluate the [RTR] feature. In (41), candidates (41c) and (41d) lose

because of the undominated markedness constraint and the word-final

faithfulness constraint, respectively. The remaining candidates are evaluated by

Spread [RTR]-L; (41a) violates this spreading constraint once since the feature

[RTR] in this candidate is not linked to one vowel. (41b), on the other hand,

incurs two violations because the [RTR] feature is not associated with two

vowels. Thus, (41) shows that the problem in (39) can be solved if privative [RTR]

is assumed.

! 152!

However, assuming [RTR] actually cannot be the solution. In fact, such an

assumption is problematic in Pulaar. First, cases such as (13) (/søf-ru/ _ [sof-ru])

cannot be explained if privative RTR is assumed; in this case, there is an [(+)ATR]

vowel word-finally, and this [(+)ATR] feature spreads to the preceding vowel.

However, if [sof-ru] competes with *[søf-ru], no mechanism selects the actual

form if [RTR] spreading is assumed; that is, the Spread [RTR]-L constraint which

is assumed in (41) is silent with respect to these two forms/candidates.

(42) presents an even more serious problem. (42) shows that Sour Grapes

arises if privative RTR is assumed; in (42), the actual surface form is (42a), where

the final and the medial vowel both surface as [(+)ATR]. However, the analysis

with privative RTR prefers (42b), where the medial vowel is identical to the

preceding vowel in the RTR/ATR specification. If privative ATR is assumed, the

case as in (41) is not a problem, but the assumption of privative RTR gives rise to

a problem in (42). ‘Removing’ directionality from the RTR-spreading constraint

makes the problem even worse since such a constraint prefers (42b), where the

spreading of RTR is more complete, than the actual form in (42a). Thus, (42)

suggests that assuming privative RTR cannot be the solution in Pulaar since the

wrong form is predicted under privative RTR.

! 153!

(42) [barø…-di]_[baro…-di]: blocker (cf. (15)) /barø…-di/ Ident [ATR]

(fin) Spread [RTR]-L

Id (Root) [RTR]

Id [RTR]

!a) b a r o… d i !!!!!!!!!!!.!!!!!!!!!!!!!! [RTR]

"b) b a r ø… d i .!!!!!!!!!!!!! [RTR]

In fact, the analyses presented in (39) and (42) suggest that it is not

possible to assume privative ATR/RTR in Pulaar if Spread is employed as a

harmony constraint; as seen in (39), if privative ATR is assumed, the candidate

with the attested leftward directionality fails. If, on the other hand, privative RTR

is assumed, then the Sour Grapes problem arises as in (42). It appears that, in

analyzing the Pulaar harmony data, it is necessary to assume that the feature

ATR is binary. This further suggests that Pulaar is one of the languages where

both [+ATR] and [-ATR] are active in harmony.

For the analysis with ABC, however, the assumption that ATR is

necessarily binary is not required; as seen in Chapter 2, ABC accounts for the

Turkish roundness harmony data even when the feature [round] is assumed to

be privative. In Pulaar ATR harmony, the following constraint in (43) accounts

for the harmony data under the assumption of privative ATR.

(43) Ident VV [ATR] (cf. Walker 2009) Let X be a segment in the output and Y be a correspondent of X in the output;

i) if X is [ATR], then Y is [ATR] ii) if X lacks the [ATR] feature, then Y lacks the [ATR] feature.

! 154!

Table 7 presents the evaluation of the Id VV [ATR] constraint under binary ATR. Table 7. The Evaluation of Id VV [ATR] Ident VV [ATR] a) a ox ix

.!!!!!!!.!!!!!!!!![ATR] [ATR]

$ (Satisfied)

b) ax ox ix

.!!!!!!!!!!.! [ATR] [ATR]

* (Violated for the pair [ax-ox])

c) ax øx ´x $ (Satisfied)

The configuration in (a) in Table 7 satisfies (48) because the two vowels in

correspondence are identical in the [ATR] feature; [o] is specified as [ATR] and [i]

is also specified as [ATR]. (c) also satisfies (48) since all the vowels in

correspondence lack the [ATR] feature (or, none of the vowels in

correspondence is specified as [ATR]). (b), on the other hand, incurs one violation

for Ident VV [ATR]; in this configuration, all the vowels are in correspondence,

and the pair [ox-ix] is identical in [ATR] specification. The [ax-ox] pair, however,

violates this faithfulness constraint since [o] is specified as [ATR] while [e] lacks

the ATR feature (thus, the [ATR] specifications of these vowels are not identical).

To summarize, for ABC, it does not make any difference whether the

feature [ATR] is assumed to be privative or binary. The analysis with Spread, on

the other hand, relies on the assumption of binary [ATR]; this further means that

the analysis with Spread predicts that Pulaar is a language where both [+ATR]

! 155!

and [-ATR] are active. One might argue that this is an unwanted prediction, since

in the majority of ATR harmony languages, there is only one active feature,

either [+ATR] or [-ATR] (or [RTR]) (cf. Archangeli and Pulleyblank 1994). I

suggest, however, that this prediction by the spreading analysis is not necessarily

problematic because, first, the Pulaar system is not dominant-recessive (note that

the claim of a single active feature is made for dominant-recessive systems), and

as pointed out, Kalenjin is also considered to be such a language. Thus, I conclude

that even though the predictions with respect to the active value of [ATR] are

different, both ABC and spreading can successfully account for the attested

harmony patterns observed in Pulaar.

4.4.3 Summary

In this chapter, I presented another case study comparing feature linking

and ABC. As demonstrated, these two approaches successfully resolve the two

empirical problems in Pulaar, namely, directionality and Sour Grapes. The

analysis presented in this chapter shows that there are two advantages of ABC

analysis; first, directionality can be accounted for with lack of correspondence

(DLC), and furthermore, the ABC analysis does not require any revisions or the

addition of any extra mechanisms. Second, ABC does not require the assumption

of binary ATR. The analysis with feature linking, on the other hand, requires

specified directionality in the spreading constraint, and the analysis crucially

relies on binary ATR. These facts, it seems, favor ABC as a comprehensive

apparatus for vowel harmony.

! 156!

However, this does not necessarily mean that Spread should be

eliminated from the OT grammar as a means of accounting for harmony. Rose

and Walker (2004) suggest that some cases of consonant harmony are more

appropriately viewed as spreading rather than long-distance agreement. If this

observation is correct, the mechanism that enforces spreading is still part of the

OT grammar. Second, it is true that the spreading analysis of ATR harmony in

Pulaar requires the assumption of binary ATR, but the universality of privative

ATR is still in question. In fact, Pulaar is not the only language in which both

[+ATR] and [-ATR] are active; as pointed out in Chapter 3, Kalenjin is also

claimed to be such a language. Hence, it is not a very wise decision to eliminate

the feature linking approach to harmony simply because of the directionality

problem and the fact that it requires binary ATR.

Rather, the aim of the remainder of this thesis, more specifically, Chapter

5, is to investigate whether ABC is actually superior to the spreading analysis as a

theory to lay out uniform and comprehensive analyses of vowel harmony. To

explore this question, roundness/backness harmony is revisited in Chapter 5. I

have shown that ABC successfully accounts for the backness and roundness

harmony in Turkish, but Chapter 5 examines the harmony processes in Yakut,

another Turkic language which is slightly different from Turkish when it comes

to roundness harmony.

! 157!

CHAPTER V ROUNDNESS HARMONY REVISITED:

A CASE STUDY OF YAKUT Thus far, I have presented two case studies, Turkish roundness/backness

harmony and Pulaar ATR harmony, and I have demonstrated that both feature

linking and ABC are capable of predicting the patterns attested in these two

languages. This leads us to ask whether both of these two approaches are

equally able to account for vowel harmony. To explore this question, in this

chapter, roundness and backness harmony are revisited via a case study of

Yakut; although the difference between Turkish and Yakut is minimal, the same

additional mechanism (an additional markedness constraint) is required in both

of these approaches to restrict the occurrence of two vowels that differ in height.

The organization of this chapter is as follows; in Section 5.1, the Yakut

backness and roundness harmony data are presented, and in Section 5.2, the

feature linking analysis is presented. The ABC analysis is presented in Section 5.3,

and a general discussion is presented in Section 5.4.

5.1 Yakut Roundness Harmony

Yakut (also known as Sakha) is a Northern Turkic language spoken in the

northern part of Siberia. It is estimated to have 363,000 speakers in the basin

along the River Lena. The major city in the Yakut-speaking region is Yakutsk

(Lewis 2009).

! 158!

As with other members of the Turkic family, vowel harmony, both

backness and roundness, is one of the major characteristics of Yakut. This section

presents the data from Yakut roundness harmony.

! The vowel inventory of Yakut is shown in Table 8. In addition to the short

vowels as presented in Table 8, there are long vowels in Yakut, and vowel length

is contrastive (Krueger 1962: 36-37). However, in vowel harmony, vowel length

does not affect the behavior of the vowels.

Table 8. Vowel Inventory of Yakut Front ([-Back]) Back ([+Back]) Non-Round Round Non-Round Round High ([+hi]) i y ! u Non-High ([-hi]) e Ø a o Source: Krueger, John (1962). Yakut Manual (Uralic and Altaic Series). Bloomington, IN: Indiana University Publication.

The vowel inventory of Yakut is completely symmetrical; all the unrounded

vowels have [round] counterparts.

In addition to the monophthongs listed in Table 8, there are four

diphthongs. These diphthongs agree in backness, but the two vowels in a

diphthong do not agree in height. In roundness harmony, the diphthongs

behave as if they were high monophthongs. The four diphthongs in Yakut are

shown in Table 9.

! 159!

Table 9. Yakut Diphthongs Front Unround Front Round Back Unround Back Round

ie yØ !a uo Source: Krueger, John (1962). Yakut Manual (Uralic and Altaic Series). Bloomington, IN: Indiana University Publication. The data in (1) illustrate total harmony, where all the vowels in a word

agree in roundness. In (1), the vowel in the accusative suffix agrees with the

preceding vowel(s) in the root not only for roundness, but also for backness

because of backness harmony. (The Yakut data presented in this chapter are

transcribed in the IPA transcription system.)

(1) Yakut Roundness Harmony: Total Harmony (Krueger 1962: 82-84)

Root Accusative1 Gloss

a. tynnyk- tynnyk-y ‘window’

b. kinige- kinige-ni ‘book’

c. murum- murum-u ‘nose’

d. bØrØ- bØrØ-ny ‘wolf’

Yakut roundness harmony is root-controlled; that is, when a root contains (a)

round vowel(s), the vowel(s) in the suffix also become(s) round. For example, in

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 The accusative suffix begins with [n] when following vowel-final roots; the [n] is absent when this suffix follows a consonant-final root (Krueger 1962: 80).

! 160!

(1a), the accusative suffix is realized as [-y] because of the round vowel in the

root, while in (1b), the same suffix is realized as [-(n)i] because of the unrounded

vowels in the root. Likewise, in (1e), where the root contains [-high, round]

vowels, the accusative suffix is [-(n)u], while in (1f), the accusative suffix is [-(n)!]

since the root does not contain any [round] vowels. The data in (1) show that

[+high, round] vowels freely follow both [+high] and [-high] round vowels. In

other words, there are no restrictions for the high round vowels in suffixes; they

are freely observed as long as the vowels in the root are [round] (regardless of

the height of the root vowels). The harmony pattern exhibited in (1) is the same

as the roundness harmony pattern in Turkish (see Chapter 2). Both in Yakut and

in Turkish, [+high, round] vowels are observed in the suffix when a root contains

a round vowel.

However, there are restrictions on the occurrence of [-high, round]

vowels in the suffixes in Yakut. As (2) shows, the [-high] vowel in the suffix is

unrounded when the closest vowel in the root is [+high] (even when the closest

vowel is round).

(2) Partial Roundness Harmony (Kaun 1995:23, Krueger 1962: 84-85)

a. tynnyk- (root) tynnyk-ler (*tynnyk-lØr) ‘window-plural’

b. tobuk- (root) tobuk-ka (*tobuk-ko) ‘knee-dative’

c. ojum- (root) ojum-tan (*ojum-ton) ‘shaman-ablative’

d. y…t- (root) y…t-yen (*y…t-yØn) ‘milk-instrumental’

! 161!

In Yakut, non-high round vowels occur in suffixes only when they are preceded

by other non-high round vowels. Thus, in (2a), for example, the vowel in the

suffix is not round because the vowels in the root are high vowels. Likewise, in

the form in (2b), the suffix vowel is unrounded because the vowel directly

preceding the suffix vowel is high. To summarize, a [-high, round] vowel is

prohibited in harmony when the trigger is [+high]. This restriction is also

observed in Turkish; thus, (2) shows that both in Yakut, and in Turkish non-high

round vowels are not observed in suffixes when the root contains (a) high round

vowel(s).

The examples in (3) show that in Yakut, diphthongs behave as if they

were high vowels, and as a result, in (3), the non-high vowel in the suffix surfaces

as unrounded.

(3) Diphthongs in Roundness Harmony (Krueger 1962: 77-81) Root Accusative Dative 2 Gloss

a. yØr- yØr-y yØr-ge (*yØr-gØ) ‘herd’

b. kyØl- kyØl-y kyØl-ge (*kyØl-gØ) ‘lake’

c. uol- uol-u uol-ga (*uol-go) ‘son’

d. muos- muos-u muos-ka (*muos-ko) ‘horn’

e. !al- !al-! !al-ga ‘neighbor’

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"!The initial consonant of the dative suffix has three variants: [-©], [-g], and [-k] (Krueger 1962: 81).

! 162!

As stated, high round vowels freely occur in suffixes as long as the vowels in the

roots are [round]. Thus, in the accusative forms in (3a) through (3d), the high

vowel in the suffix is [round]. In the dative forms, where the suffix contains a

non-high vowel, on the other hand, the vowel in the suffix is unrounded in (3a)

through (3d). Thus, the data in (3) show that the diphthongs in Yakut function in

the same way as high vowels, and if there is a non-high vowel in a suffix, then

that vowel surfaces as unrounded. In other words, a non-high round vowel may

not follow a diphthong in Yakut.

The data in (2) and (3) show that in Yakut and in Turkish, a similar

restriction is observed in the occurrence of non-high round vowels. The data in

(4) show, however, a roundness harmony pattern which is attested in Yakut but

not in Turkish.

(4) A Non-high Round Vowel in a Suffix (Krueger 1962: 72-75)

b. bØrØ- (root) bØrØ-lØr (*bØrØ-ler) ‘wolf-plural’

c. Øj- (root) Øj-tØn (*Øj-ten) ‘reason-ablative’

In Yakut, the non-high vowel in the suffix is round when it is preceded by

another non-high round vowel in the root. Thus, in (4a), the plural suffix contains

a non-high round vowel because of another non-high round vowel in the root.

Notice that this pattern is not attested in Turkish, as seen in the data in (5)

(repeated from (2) in Chapter 2)

! 163!

(5) Turkish Roundness Harmony (Clements and Sezer 1982: 216)

Root Genitive Plural Gloss

a. kØj kØ-yn kØj-ler (*kØj-lØr) ‘village’

b. son son-un son-lar (*son-lor) ‘end’

(4) and (5) show the difference between Yakut and Turkish. Unlike Yakut,

Turkish does not allow any roundness harmony pattern in which a non-high

round vowel is observed in a suffix. In Yakut, on the other hand, non-high round

vowels can be observed in suffixes when preceded by a [-high, round] root

vowel.

Table 10 summarizes the attested and the prohibited roundness harmony

patterns in Yakut roundness harmony.

Table 10. Restrictions on Roundness Harmony in Yakut Attested Not Attested Front Vowels -y-y

(both [+hi]) - y-e

Ø-y ([-hi] > [+hi])

Ø-Ø (both [-hi])

*y-Ø ([+hi] >[-hi])

Back Vowels -u-u (both [+hi]) - u-a

o-u ([-hi ] >[+hi])

o-o (both [-hi])

*u-o ([+hi] > [-hi])

The next two sections consider how feature linking and ABC account for

the harmony patterns observed in Yakut roundness harmony. I assume that the

feature [round] is privative, as assumed in Chapter 2 and in other previous

accounts of roundness harmony.

! 164!

5.2 The Analysis with Spread

5.2.1 Roundness Harmony

First, this section presents the feature-linking analysis of Yakut roundness

harmony. The harmony constraint in (6) is used.

(6) Spread [Round] (cf. Padgett 1997, 2002; Sasa 2001) If a feature [round] is associated with a vowel, the same roundness feature is linked to all of the vowels in a word.

The constraint in (6) is satisfied when all the vowels in the output share the same

roundness feature.

As seen in the data, Yakut roundness harmony is root-controlled. Thus,

the positional faithfulness constraint in (7) preserves the identity of the trigger.

(7) Ident I-O [round] (!1) (Id (!1) [round]) (cf. Beckman 1997, 1998; Sasa 2001) Segments in the initial syllable of a word in the output have the same specification as their input correspondents for the feature [round].

The same effect would be achieved by a root faithfulness constraint, but since

there are no disharmonic roots in Yakut, I assume the initial syllable faithfulness

constraint in (7) to preserve the input identity of the trigger.

In addition to the positional faithfulness constraint for roundness, the

general faithfulness constraint for the roundness feature in (8) is also part of the

grammar.3

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!#!In addition to (8), I assume that another faithfulness constraint, Ident [hi], is undominated in Yakut, since changing vowel height is not attested to achieve complete harmony.

! 165!

(8) Ident [round] (Id [round]) (McCarthy and Prince 1995) Correspondent input and output segments have the same specification for the feature [round].

As seen in the data, there are restrictions on the occurrence of the [-high,

round] vowels. The markedness constraint in (9) is also active in accounting for

the attested data in Yakut.4

(9) *o/Ø (cf. Kaun 1995) Non-high [round] vowels are prohibited.

The analysis for total roundness harmony is presented in (10).!!

(10) Total harmony: both trigger and target are [+high] /tynnyk-i/ Id (!1) [Round] Spread [round] Id [round]

!a) tynnyk-y ! [round]

b) tynnyk-i ! [round]

c) tinnik-i *! ** d) tynnik-i $! [round]

In (10), candidate (10c) is ruled out because of the positional faithfulness

constraint. In (10b), the [round] feature is associated with two vowels in the root,

but this [round] feature is not linked to the vowel in the suffix. As a result, this

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!%!One might ask, given the markedness constraint in (9), how it is possible to observe [-high] round vowel in Yakut. It is possible for non-high round vowels to appear when i) they occur in the initial syllable of a word (protected by (7), if an input contains a [-high, round] vowel in that position) or ii) when the spreading of the [round] feature to non-high vowels in other positions (for example, in suffixes) is not blocked by another markedness constraint (*H-L [round] in (15) below).

! 166!

candidate incurs one violation for Spread [round]. Likewise, even though (10d)

satisfies the positional faithfulness constraint for the first syllable, this candidate is

ruled out because of the spreading constraint. Candidate (10a), the actual form,

satisfies both the positional faithfulness constraint and the spreading constraint,

but violates the general faithfulness constraint for the roundness feature.5

The tableau in (11) illustrates the analysis of another case of total harmony,

where the trigger and the target of the harmony are [-high]. In (11), the

markedness constraint prohibiting [-high, round] vowels is also included in the

tableau.

for the spreading constraint while (11a), the actual form, fully satisfies this

constraint. Thus, Spread [round] prefers (11a) to (11b).

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!&!In (10), there are other possible candidates from the same input. For example, *[tynnyk-u] is a logically possible candidate. However, Spread [back] excludes such a candidate. The discussion of backness harmony with spreading is presented in Section 5.2.2. !

! 167!

In (12), the third case of total harmony, where the trigger is a [-high]

vowel and the target is a [+high] vowel, is presented. In Yakut, high round

vowels freely occur in suffixes even when the root contains a [-high, round]

vowel. Therefore, the actual form contains a high round vowel in the suffix in

(12) even though the vowels in the root are [-high] round vowels. The initial

syllable faithfulness constraint excludes (12c), and the spreading constraint

prefers (12a) to (12b).

(13) shows the summary of the ranking arguments presented in the

analyses in (10) through (12).

(13) Ranking Argument 1 - Spread [round] >> Ident [round] (from (10)) - Spread [round] >> *o/Ø (from (11)) - Ident (!1) >> *o/Ø (from (12)) The analysis with Spread [round] successfully accounts for total harmony.

However, as seen in (14), the analysis presented thus far fails to account for the

partial harmony case, that is, the pattern where the trigger is [+high] and the

target is [-high]; in (14), the spreading constraint prefers (14c), in which the non-

! 168!

high vowel in the suffix undergoes harmony when the vowel in the root is

[+high, round]. However, such a pattern is not observed in Yakut.

(14) Partial harmony: [-high] suffix vowel does not participate in the harmony /tynnyk-ler/ Id (!1) [round] Spread [round] *o/Ø Id [round]

!a) tynnyk-ler !!!!!!!!!!!!'()*+,-!

b) tinnik-ler *! ** "c) tynnyk-lØr !!!!!!!!!!!!!'()*+,-!

Candidate (14b) is excluded because of the initial syllable faithfulness constraint.

Candidate (14a), the actual form, loses because of Spread [round]; there is a

[round] feature associated with the vowels in the root, but this [round] feature is

not linked to the vowel in the suffix. (14c) completely satisfies this harmony

constraint, and as a result, (14c) is wrongly selected as the optimal candidate.

As shown in (11), it is not possible to reverse the ranking for Spread

[round], *o/Ø, and Ident [round]. As (11) shows, the markedness constraint

against non-high round vowels must be dominated by the spreading constraint,

and Spread [round] also must dominate the general faithfulness constraint for

the roundness feature, as shown in (10).

To resolve this issue in Yakut, Sasa (2001) proposes a markedness

constraint which prohibits the multiple linking of the [round] feature to vowels

that are different in height. This proposed markedness constraint is presented in

! 169!

(15) *High-Low [round] (*H-L [round]) (Sasa 2001: 277) If the feature [round] is linked to a high vowel, the same [round] feature is not linked to a following non-high vowel.

Figure 16 illustrates the satisfaction and violation patterns of (15). The

configuration in (a) in Figure 16 does not violate *H-L [round] because the two

vowels (V1 and V2) do not differ in height. (b) also satisfies this constraint

because the precedence relationship in this configuration does not match the

description given in the definition of this constraint; that is, if the first vowel in a

pair is [-high], the constraint in (15) is silent on such a configuration. This is true

even if two vowels are different in height but still share the same [round] feature.

(c) violates *H-L [round]; in this configuration, the first vowel, V1, is specified as

[+high], and the following vowel, V2, is specified as [-high]. The markedness

constraint in (15) prohibits the sharing of the same [round] feature if two vowels

are in this particular precedence relationship.

a) b) c) [-high] [-high] [-high] [+high] [+high] [-high] V1 V2 V1 V2 V1 V2 [round] [round] [round] # (Satisfied) # (Satisfied) * (Violated) Figure 16. The Evaluation of *High-Low [round]

! 170!

Sasa (2001) suggests that the markedness constraint in (15) is half of the

following constraint in (16).

(16) Uniformity Round (cf. Kaun 1995) [round] may not be multiply linked to slots if slots are different in height. (16) prohibits the configurations in (b) and (c) of Figure 16, where the same

[round] feature is associated with two vowels of different heights. However, in

Yakut, it is true that the configuration in (c) in Figure 16 is not attested, but that

in (20b) is an attested pattern. Therefore, Sasa suggests that (16) should be split

into two, one half prohibiting (20b), and the other half prohibiting (20c). Sasa

suggests that *H-L [round], which prohibits only (c) in Figure 16, is active in the

grammar of Yakut.6

The analysis with (15) is presented in the tableau in (17).

(17) Partial harmony: non-high target does not participate in harmony (when the trigger is [+high]) /tynnyk-ler/ Id (!1)

[round] *H-L

[round] Spread [round]

*o/Ø Id [round]

$ a) tynnyk-ler !!!!!!!!!"()*+,-!

b) tynnyk-lØr !!!!!!!!'()*+,-!

c) tinnik-ler *! ** d) tynnyk-lØr $ [round][round]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.!This issue is discussed further in Section 5.4.2 of this chapter.

! 171!

(17c) loses because of the positional faithfulness constraint for the initial syllable.

(17b) loses because of the *H-L [round] constraint; in this candidate, the [round]

feature associated with the preceding high vowels is simultaneously associated

with the following non-high vowel. In (17d), on the other hand, the [round]

feature associated with the high vowels is not simultaneously associated with a

non-high vowel; instead, a different [round] feature is associated with the non-

high vowel in the suffix. Thus, (17d) does not violate *H-L [round]. However,

(17d) loses because of the spreading constraint since the [round] feature

associated with the high vowels in the root is not associated with the vowel in

the suffix (one violation) and the roundness feature associated with the non-high

vowel in the suffix is not linked to the vowels in the root (two violations). (17d)

incurs three violations for *H-L [round] in total, and as a result, (17a), the actual

form, is selected as optimal.

Another analysis of partial harmony is presented in (18). In (18), the input

contains a round vowel in the suffix.

(18) Partial harmony 2: input with a non-high round vowel in the suffix /tynnyk-lØr/ Id (!1)

[round] *H-L

[round] Spread [round]

*o/Ø Id [round]

!a) tynnyk-ler !!!!!!!!!!!!

!!!!!!!!!'()*+,-!

b) tynnyk-lØr !!!!!!!!!!'()*+,-!

c) tynnyk-lØr !!!!!!!!!!!!!!!!!$!'()*+,-!!'()*+,-!

! 172!

In (18), all the candidates satisfy the initial syllable faithfulness constraint. (18b)

violates the *H-L [round] constraint; in this candidate, the same [round] feature is

associated with vowels of different heights, and [+high] vowels precede the non-

high vowel. Candidate (18c) satisfies *H-L [round] (although the phonetic

realization of this candidate is the same as that of (18b)); it is true that the non-

high vowel in the suffix is specified as [round], but the suffix vowel in this

candidate does not share the [round] feature associated with the preceding high

vowels. This candidate, however, incurs three violations of Spread [round]. As a

result, the spreading constraint prefers the actual form to the candidate in (18c).

The summary of the constraint ranking that accounts for Yakut roundness

harmony is presented in Figure 17.

Ident (!1) [round] *H-L [round] Spread [round] !

! ! ! ! !/o/Ø Ident [round] Figure 17. Ranking Lattice: Yakut/Spread

In Yakut, the ranking Spread [round] >> Ident [round] enforces harmony.

However, changing the roundness specification of the root vowels is not an

attested method of satisfying Spread [round]. This is expressed by the ranking

where the initial syllable faithfulness constraint dominates the spreading

! 173!

constraint. These two mechanisms are the same in Turkish as well, except that

root faithfulness, rather than initial syllable faithfulness, is assumed in Turkish.

The crucial difference between Yakut and Turkish is the ranking of the

markedness constraint:

(19) Ranking for Yakut and Turkish

a) Turkish: Ident (root) [round] >> *o/Ø >> Spread [round]

b) Yakut: Ident (!1) [round] >> Spread [round] >> *o/Ø

In Turkish, the suffix vowel is always unrounded if it is non-high; this is captured

by the ranking in which the markedness constraint dominates the spreading

constraint. In Yakut, on the other hand, the non-high vowel in the suffix can be

round when the vowel(s) in the root is/are also [-high].7 As (19) shows, therefore,

the markedness constraint cannot dominate the spreading constraint, or else the

suffix non-high vowel would be always unrounded.

However, if the spreading constraint dominates the markedness

constraint, such a ranking predicts that all the suffix vowels become round when

there is a round vowel in the root. This is not the pattern observed in Yakut.

Thus, another ranking, *H-L [round] >> Spread [round], also must be established

so that total roundness harmony is achieved in two cases: i) both the trigger and

the target agree in height, or ii) the trigger is non-high and the target is high. The

analysis presented in this section suggests that assuming a markedness !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!0!Except when the root contains a diphthong.

! 174!

constraint prohibiting feature-sharing (that is, *H-L [round]) plays a crucial role

in accounting for the blocking effect in harmony, where certain vowels do not

participate in the harmony process.8

5.2.2 Backness Harmony

To account for backness harmony, which is observed in Yakut in addition

to roundness harmony, another spreading constraint, as in (20), is necessary.9

(20) Spread [back] (cf. Padgett 2002: 89) If a feature [+back] or [-back] is associated with a vowel, the same backness feature is linked to all the vowels in a word.

The analysis with (20) is presented in (21). In (21), candidate (21c) loses

because of the Spread [back] constraint; the [-back] feature associated with the

root vowels is not associated with the suffix vowel (one violation) and the [-back]

feature of the suffix vowel is not linked to two vowels in the root (additional two

violations). Candidate (21d) satisfies the spreading constraint for the backness

feature, but this candidate loses because of the initial syllable faithfulness

constraint. The remaining two candidates satisfy both the positional faithfulness

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1!Kaun (1995) presents an analysis of Yakut roundness harmony with the constraints Extend [round] if [-high] (“[round] must be associated with all available vocalic positions within a word when simultaneously associated with [-high]”) and Uniform [round] (listed in (16)), instead of assuming *H-L [round]. Sasa (2001) points out, however, that the analysis with these two constraints encounters a ranking paradox in Yakut. 2!It is also possible to achieve both roundness and backness harmony by assuming i) the feature class [color] (which contains [back] and [round] features as a terminal node), and ii) the spreading constraint Spread [color] (Padgett 2002: 89). The harmony constraint Spread [color] is discussed in Chapter 6.

! 175!

constraint and the spreading constraint for backness, but *H-L [round] prefers

the actual form.

(21) Backness harmony: no disharmonic forms /tynnyk-lar/ Id (!1)

[back] Spread [back]

*H-L [round]

Spread [round]

Id [back]

!a) tynnyk-ler !!!!!!!!!!!!

!!!!!!!!!'34567-!

b) tynnyk-lØr !!!!!!!!!!'34567-!

c) tynnyk-lar !!!!!!!!!!!!!!!!!$!'34567-!!'84567-!

d) t!nn!k-lar [+back]

It has been demonstrated that the spreading analysis is capable of

accounting for the attested patterns of roundness harmony and backness

harmony in Yakut. Section 5.3 illustrates the ABC analysis of Yakut, and

discusses the challenge that an ABC analysis encounters in the Yakut harmony

processes.

5.3 Agreement By Correspondence

The focus of Section 5.3 is a discussion of the ABC treatment of Yakut

roundness harmony and backness harmony. The ABC analysis faces one issue in

accounting for roundness and backness harmony in Yakut; the mechanism

necessary to account for roundness harmony is problematic in accounting for

backness harmony. The mechanism (more specifically, the constraint ranking

necessary for backness harmony) selects the wrong form as a winner. In other

! 176!

words, a ranking paradox is observed in the ABC analysis of Yakut. However, I

demonstrate that this ranking paradox can be resolved by assuming *H-L

[round] (which accounts for the restriction on the occurrence of the [-high,

round] vowels in the spreading analysis).

The organization of this section is as follows; the full ABC analysis of

roundness harmony is presented in Section 5.3.1; Section 5.3.2 gives a

presentation of the ABC analysis of backness harmony and the problems with

the ABC account of Yakut harmony.

5.3.1 The ABC Analysis of Yakut Roundness Harmony

The pattern in Yakut roundness harmony is slightly more complicated

than the Turkish pattern in that it is possible to observe non-high round vowels

in suffixes (when the trigger is non-high), which is not attested in Turkish. The

following output correspondence constraints need to be assumed to allow non-

high vowels to be round in some cases, while prohibiting them from being

round in other cases. The necessity of (22a) and (22b), independently of (22c), is

shown in the analyses in (27) and (28).

(22) a. Correspond [+high]-[+high] (Corr [+hi]) (cf. Walker 2009) Let S be an output string of segments and let X and Y be [-consonantal, +high] segments. If X and Y belong to S, then X and Y correspond.

b. Correspond [-high]-[-high] (Corr [-hi]) (cf. Walker 2009)

Let S be an output string of segments and let X and Y be [-consonantal, -high] segments. If X and Y belong to S, then X and Y correspond.

! 177!

c. Correspond V-V (Corr V-V) (cf. Rose and Walker 2004: 491) Let S be an output string of segments and let X and Y be [-consonantal]. If X and Y belong to S, then X and Y correspond.

The output identity constraint in (23) requires that segments in

correspondence be identical in roundness.

(23) Ident VV [round] (Id VV [round]) (cf. Rose and Walker 2004: 492, Walker 2009) Let X be a segment in the output and Y be a correspondence of X. If X is [round], then Y is [round].

In addition to the ABC constraints listed in (22) and (23), the following OT

constraints, which were introduced in the spreading analysis, are also necessary

for an ABC analysis.

(24) a. Ident I-O [round] (!1) (Id (!1) [round]) Segments in the initial syllable of a word in the output have the same specification as their input correspondents for the feature [round].

b. Ident [round] (Id [round])

c. *o/Ø

Non-high [round] vowels are prohibited. The tableau in (25) presents the ABC analysis for the total harmony

pattern, where both the trigger and the target are [+high].

(25) Total harmony 1: trigger and target are both [+high] /tynnyk-i/ Id (!1)

[round] Corr [+hi] Id VV

[round] Id I-O

[round]

!a) tyxnnyxk-yx * b) tyxnnyxk-i *! c) tixnnixk-ix *! ** d) tyxnnyxk-ix *!

! 178!

In candidate (25a), all the vowels are in correspondence and thus, Corr

[+hi] is satisfied. All the vowels in (25c) are also in correspondence, but this

candidate loses because of the initial syllable faithfulness constraint. (25b) violates

Corr +Hi because in this candidate, not all high vowels are in correspondence.

More specifically, the high vowel in the suffix and the high vowels in the root do

not correspond. Finally, the candidate in (25d) satisfies the correspondence

constraint, but this candidate is ruled out because of the Ident VV constraint; in

(25d), not all the vowels in correspondence are identical with respect to the

feature [round]. (25) shows that Corr [+hi] dominates the general faithfulness

constraint for [round] (Corr [+hi] >> Ident I-O [round]), and also that the

correspondent identity constraint is ranked above the I-O faithfulness constraint

for the roundness feature (Ident V-V [round] >> Ident [round]).10

(26) shows the analysis of another total harmony case, in which both the

trigger and the target are [-high].

[round] Corr [+hi]

Corr [-hi]

Id VV [round]

*o/Ø Id [round]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9:!In (25), there is another logically possible candidate from the same input, [tyxnnyxk-ux]. I assume that these candidates are excluded by the Ident VV [back] constraint. A detailed discussion is presented in Section 5.3.2. !

! 179!

All of the non-high vowels in (26a) are in correspondence. In (26b), the vowel in

the suffix is not in correspondence with the non-high vowels in the root, and

thus, this candidate violates Corr [-hi]. (26c), on the other hand, satisfies the

correspondence constraint for non-high vowels since all the vowels in this

candidate are in correspondence. However, this candidate loses because of the

Ident VV [round] constraint; in this candidate, it is true that all the vowels are in

correspondence, but the vowels in correspondence are not identical in the

[round] feature. As a result, both Corr [-hi] and Ident VV [round] select the

actual form in (26a), where all the non-high vowels surface as [round]. (26)

shows that both Corr [-hi] and Ident VV [round] dominate the markedness

constraint, *o/Ø (Corr -Hi, Ident VV [round] >> *o/Ø).

(27) shows another analysis for total harmony, but in (27), the trigger and

the target do not agree in height.

[round] Corr [+hi]

Corr [-Hi]

Id VV [Rd]

*o/Ø Corr V-V

Id [round]

!a) ox©ox-nux ** * b) ox©ox-n! ** *! c) ax©ax-n!x *! ** d) ox©ox-n!x *! ** (27) shows that the established ranking Ident VV [round] >> *o/Ø functions to

select the attested form in (27a) over one of the unattested forms/candidates,

which is in (27d). Candidate (27d) satisfies the initial syllable faithfulness

constraint and all the correspondence constraints, as does the actual form (27a),

! 180!

but (27d) loses because of the identity constraint for segments in output

correspondence; in (27d), all the vowels are in correspondence but the suffix

vowel is not identical to the rest of the correspondent vowels in roundness

specification. Ident VV [round] excludes (27d).

Even though (27c) satisfies all the correspondence constraints and the

markedness constraint, it loses because of the initial syllable faithfulness

constraint. Candidate (27b), the remaining competitor, also satisfies both Corr

[+hi] and Corr [-hi], and (27b) and (27a) tie under the markedness constraint.

However, (27b) loses because of Corr V-V (which requires that all the vowels be

in correspondence regardless of height), since in this candidate, not all vowels are

in correspondence, while (27a) satisfies this correspondence constraint. Thus, as

seen in (25) through (27), the analysis with ABC is capable of predicting the total

harmony pattern in Yakut roundness harmony. As seen in (27), ABC correctly

predicts total harmony even when trigger and target do not agree in height.

Finally, the analysis of partial harmony is presented in (28).

(28) Partial harmony: Ident VV, *o/Ø >> Corr V-V blocks the unattested patterns /tynnyk-lØr/ Id(!1)

[round] Corr [+hi]

Corr [-Hi]

IdVV [Rd]

*o/Ø Corr V-V

Id [round]

!a) tyxnnyxk-ler

b) tyxnnyxk-lØxr *! c) tyxnnyxk-lØr *! * d) tyxnnyxk-lexr *! * In (28), candidate (28a) contains one vowel in the suffix which is not in

correspondence with other vowels. In (28b) and (28d), all the vowels are in

! 181!

correspondence. In (28c), the suffix vowel is not in correspondence but in this

candidate, unlike (28a), the suffix vowel is [round]. (28d) loses because of Ident

V-V since not all the vowels in correspondence are identical in the [round]

feature. Both (28b) and (28c) satisfy all of Corr +Hi, Corr -Hi, and Ident V-V, but

these candidates are excluded by the markedness constraint for the non-high

[round] vowels. (The markedness constraint *o/Ø assigns violations to a

candidate which contains these vowels; it does not any make difference whether

the non-high round vowels are in correspondence with other vowels or not.) As

a result, candidate (28a) is selected as optimal even though not all vowels are in

correspondence in this candidate (that is, Corr V-V is violated). (28) shows that

the markedness constraint, *o/Ø, dominates Corr V-V and the general

faithfulness constraint for roundness.

In (28), the non-participating vowel does not correspond to other vowels

in the word. In other words, the correspondence relation is absent between the

participating vowels and the non-participating vowel. This is expressed by the

ranking *o/Ø >> Corr V-V, which states that avoiding marked vowels is more

important than all the vowels being in correspondence. The blocking effect in

roundness harmony, as a result, is explained through the lack of correspondence

that results from this ranking. I suggest that in roundness harmony, the blocking

effect (that is, certain vowel(s) do/does not participate in harmony) is accounted

for by Blocking by Lack of Correspondence (BLC).

! 182!

Figure 18 provides the ranking lattice for the ABC analysis. The

established ranking correctly predicts the occurrence of the non-high round

vowels in Yakut; [-high, round] vowels freely occur in roots, and this is captured

by the high-ranked initial syllable faithfulness constraint.

Corr [+hi] Corr [-hi] Ident (!1) [round] Ident V-V [round] *o/Ø $!! ! ! ! !!!!!!!!!!!Corr V-V $!! ! ! ! ! Ident I-O [round] Figure 18 Ranking Lattice: Yakut/ABC

A similar restriction is observed in Turkish as well, but the difference between

Yakut and Turkish is that in suffixes, non-high round vowels are allowed only

when the trigger (that is, the round vowel in the root) is also non-high in Yakut.

This difference is captured by the ranking of the markedness, output

correspondence and output identity constraints, as shown in (29).

(29) Ranking in Yakut and Turkish (ABC analysis)

a) Turkish: Ident (root) [round] >> *o/Ø >> Ident VV [round]

b) Yakut: Ident (!1) [round] >> Ident VV [round] >> *o/Ø

! 183!

The ranking Ident (root) [round] >> *o/Ø in Turkish correctly captures the fact

that non-high round vowels are prohibited except in the root. The ranking Ident

VV [round] >> *o/Ø in Yakut predicts that non-high round vowels are allowed in

suffixes only when they are in correspondence with the vowels in the root. As

seen in the analysis, this prediction is true. To exclude the unattested combination

of round vowels, output correspondence constraints specific to height need to be

assumed (and high-ranked) in addition to the general correspondence constraint,

Corr V-V.

The key claim made in this section is that the blocking effect in roundness

harmony can be explained through Blocking by Lack of Correspondence (BLC).

This mechanism in the ABC analysis is totally different from the mechanism in

the spreading analysis; the spreading analysis crucially relies on the markedness

constraint, *H-L [round]. In the ABC analysis, on the other hand, the blocking

effect can be accounted for without this markedness constraint when it comes

only to roundness harmony.

Thus, it seems that the ABC analysis is superior to the Spread account

because it does not require such a markedness constraint. However, as seen in

the next section, BLC cannot account for both roundness harmony and backness

harmony. The problem with BLC is discussed in the next section; I suggest, as a

solution to the BLC problem, that the effect of *H-L [round] is the key to solving

the problem.

! 184!

5.3.2 The ABC Account of Backness Harmony

As seen in the case study of Turkish, the output identity constraint for the

backness feature requires that vowels in correspondence be identical in backness,

and thus, enforces harmony. The output identity constraint for the backness

feature is presented in (30).

(30) Ident VV [back] (Id VV [back]) (cf. Rose and Walker 2004: 492, Walker 2009) Let X be a segment in the output and Y be a correspondent of X. If X is [+back], then Y is [+back]. If X is [-back], then Y is [-back].

The analysis with (30) is presented in (31). In (31), the faithfulness

constraints, both for input-output and for output correspondence, refer to

backness rather than roundness.

(31) Backness harmony 1 /tynnyk-u/ Id (!1)

[back] Corr [+hi] Id VV

[back] Id

[back]

!a) tyxnnyxk-yx * b) tyxnnyxk-u *! c) t!xnn!xk-!x *! ** d) tyxnnyxk-ux *! In (31), the initial syllable faithfulness constraint excludes (31c) from the

competition. Candidates (31b) and (31d), in which the suffix vowel is not identical

to the root vowels in backness, are excluded by Corr [+hi] and the output

identity constraint for backness, respectively. As a result, the actual form in (31a)

is selected as a winner, since all the vowels are in correspondence and are

identical with respect to backness.

! 185!

(31) shows that the Ident VV [back] constraint plays a crucial role in

selecting a candidate in which all the vowels agree in backness. However, the

effects of the output identity constraints are visible only when vowels are in

correspondence. This point is illustrated in (32). In (32), for the sake of argument,

the input vowel in the suffix, /A/, is unspecified for backness and roundness and

it is assumed that the I-O faithfulness constraint is violated if an output

correspondent is specified either for backness or roundness.11 In (32), the initial

syllable faithfulness constraint is not included in the tableau because of space

limitations, but all the candidates satisfy this positional faithfulness constraint.

(32) Roundness AND backness harmony /tynnyk-lAr/ Id VV

[back] Corr [+hi]

Corr [-hi]

IdV-V [Rd]

*o/Ø Corr V-V

Id [back]

! a) tyxnnyxk-ler * * b) tyxnnyxk-lØxr *! * c) tyxnnyxk-lar * * d) tyxnnyxk-laxr *(!) *(!) * The actual surface form in (32) is (32a), in which all the vowels are [-back] (and

the suffix vowel is unrounded) but (32a) and (32c) tie in this evaluation.

Candidate (32b) loses because of the markedness constraint, and the Ident VV

[back] constraint excludes (32d), in which all the vowels are in correspondence

but not identical in backness. Ident VV [back], however, is silent with respect to

candidate (32c) because the suffix vowel is not in correspondence and the root

vowels, which are in correspondence, are identical in backness. (32a) and (32c)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!99!Once again, nothing hinges on this assumption.

! 186!

both violate Corr V-V and they both violate the input-output faithfulness

constraint for backness. As a result, neither one of these candidates is selected as

optimal in (32).

One might suggest the re-ranking Corr V-V to exclude a candidate such as

in (32c) (since in (32a), not all of the vowels are in correspondence); this solution

is investigated in (33), in which Corr V-V now dominates Ident VV [round] and

the markedness constraint. It is true that re-ranking of Corr V-V does succeed in

excluding a candidate such as (33c), but this cannot solve the whole problem in

(32); as seen in (33), the established ranking Ident VV [Rd] >> *o/Ø still prefers

(33b) to the actual form in (33a).

(33) Roundness AND backness harmony: ranking paradox /tynnyk-lAr/ Id VV

[back] Corr +Hi

Corr -Hi

Corr V-V

Id VV [Rd]

*o/Ø Id[back]

!a) tyxnnyxk-lexr *! * "b) tyxnnyxk-lØxr * * c) tyxnnyxk-lar *! * d) tyxnnyxk-laxr *! *

% & Ranking Paradox orz (cf.(26))

In (33), two constraints, Ident VV [back] and Corr V-V, eliminate the candidates

in which backness harmony is not observed; (33c) is ruled out because of the

correspondence constraint, and (33d) is excluded because of the output

correspondent identity constraint.

However, the ranking Ident VV [round] >> *o/Ø prefers candidate (33b),

where the suffix vowel undergoes harmony. The actual form, (33a), violates the

! 187!

Ident VV [round] constraint because the vowels in correspondence are not

identical with regard to roundness in this candidate. Candidate (33b), on the

other hand, satisfies this faithfulness constraint since all the vowels in

correspondence are identical in roundness.12 As seen in (26) above, the

markedness constraint prohibiting [-high, round] vowels needs to be ranked

lower than the Ident VV [round] constraint. In (33), the reverse ranking (*o/Ø >>

Ident VV [round]) is required to select the actual form. Thus, (33) shows that

forcing vowels to be in correspondence cannot provide the complete solution to

backness harmony, and in fact, if vowels are in correspondence, a ranking

paradox is observed; to account for backness harmony, the markedness

constraint needs to dominate the output faithfulness constraint. In accounting for

roundness harmony, on the other hand, the markedness constraint needs to be

dominated by the output faithfulness constraint.

The problem with the candidate in (33b) is that an illicit combination of the

round vowels is observed in this candidate. I suggest that this problem can be

solved by assuming the markedness constraint in (34).

(34) *High-Low [round] (*H-L [round]) (repeated from (15)) If the feature [round] is linked to a high vowel, the same [round] feature is not linked to a following non-high vowel.

However, in ABC, feature linking is not necessarily assumed. Thus, the original

formulation of *H-L [round] in (34) does not resolve the issue. (That is, (34) is a !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9"!Even if the feature class [color] (cf. Padgett 2002) and Id VV [color] (which requires that correspondent vowels be identical in backness and roundness) are assumed in (33), candidate (33b) is still preferred to the actual form in (33a).

! 188!

valid solution when feature linking is assumed, as in the spreading analysis.)

Thus, I suggest the revised markedness constraint in (35).

(35) *High-Low [round] (*H-L [round]) (revised) In a sequence of two round vowels, if the first is [+high], the second is also [+high]. (A high round vowel may not be followed by a non-high round vowel.)

A solution, adopting (35), is presented in (36). 13 (In (36), some of the

constraints included in (33) are not included due to space limitations.)

(36) Roundness AND backness harmony /tynnyk-lAr/ Id VV

[back] *H-L

[round] Corr V-V

IdVV [Rd]

*o/Ø Id [back]

a) tyxnnyxk-lexr * * b) tyxnnyxk-lØxr *! * * c) tyxnnyxk-lØr *(!) *(!) * d) tyxnnyxk-laxr *! * In (36), the ranking *H-L [round] >> Id VV [round] selects the attested form.

Candidate (36d) loses because of the correspondence identity constraint for

backness. Both (36b) (in which all the vowels are in correspondence) and (36c) (in

which the suffix vowel is not in correspondence) lose because of the *H-L

[round] constraint; in these, two [round] vowels are not identical in height when

the preceding vowel, namely, the vowel in the root, is [+high]. As a result, the

attested surface form is selected as optimal (as mentioned, it does not make a

difference whether a non-high round vowel is in correspondence in the

assessment of a markedness constraint such as *H-L [round]).

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9#!The Uniformity [round] constraint presented in (16) cannot be the solution in (33); in Yakut, the sequence of [-high]-[+high] round vowels is permissible, and it is not always the case that two round vowels are identical in height.

! 189!

5.4 Discussion

5.4.1 Summary of the Chapter

Thus far, I have demonstrated that both spreading and ABC are able to

handle the data in Yakut backness and roundness harmony. I pointed out that

both of these two approaches crucially rely on some version of a *H-L [round]

constraint.

In the feature linking analysis, this markedness constraint is indispensable

in accounting for roundness harmony. In the ABC analysis, on the other hand, it

seemed as though such a constraint was unnecessary; as seen in Section 5.3.1, the

blocking effect in roundness harmony can be attributed to a lack of

correspondence. However, *H-L [round] is actually required in the ABC account

of backness harmony in Yakut. This suggests two points. First, in Yakut, in which

the markedness constraint *o/Ø cannot dominate the spreading constraint or the

ID VV [round] constraint, an additional markedness constraint is necessary to

restrict the occurrence of non-high [round] vowels in suffixes. In other words,

without a constraint that refers to the height of round vowels, both ABC and the

spreading analysis fail to account for the restrictions on the occurrence of non-

high vowels.

This further suggests that there may be some (universal) tendency to

avoid sequences of round vowels if they are not identical in height. Kaun (1995),

for example, presents a typological analysis of roundness harmony using

Uniformity [round] (cf. (16)). In Section 5.2.1, however, I argued that this

! 190!

uniformity constraint should be split into two separate markedness constraints.

As seen in Section 5.2.1, one half of the uniformity constraint,*H-L [round] (or its

revised version), is active in Yakut. Provided this, one may ask an additional

question: are there any languages where the other half of the uniformity

constraint is active? This question is examined in the next section.

5.4.2 A Residual Issue

In Section 5.2, I suggested that Uniformity [round] should be split into two

separate constraints: one that prohibits the combination of high-low (non-high)

round vowels and another that prohibits a sequence of low-high round vowels.

This leads us to ask whether there are any languages where the other half of

Uniformity [round], namely, the constraint in (37), is active.

(37) *Low-High [round] (*L-H [round]) If the feature [round] is linked to a non-high vowel, the same [round] feature is not linked to a following high vowel.

If there are languages that require the constraint in (37), that would give

additional support to the analyses of Yakut presented in this chapter, since the

existence of such languages suggests that the uniformity constraint must be split

into two separate constraints. I suggest that Kachin Khakass (northern Turkic,

Korn 1969) appears to be an example of such a language, and I present both

spreading and ABC analyses of Kachin Khakass in this section.

The roundness harmony patterns in Kachin Khakass are summarized in

Table 11, and the data are presented in (38) and in (39); as Korn (1969) points out,

Kachin Khakass exhibits both backness and roundness harmony (as in other

! 191!

Turkic languages), and the forms in (38) and (39) also show that the vowel in the

suffix agrees with the root vowel in backness.14

Table 11. Restrictions on Roundness Harmony in Kachin Khakass Attested Not Attested Front Vowels y-y

(both [+hi]) *Ø-y ([-hi] >[+hi])

*Ø-Ø (both [-hi])

*y-Ø ([+hi] > [-hi])

Back Vowels u-u (both [+hi])

*o-u ([-hi] >[+hi])

*o-o (both [-hi])

*u-o ([+hi] > [-hi])

(38) Kachin Khakass Roundness Harmony 1 (Korn 1969: 102)

a. kuß-tu˜ (*kuß-t!˜) ‘of the bird’

b. kyn-ny (*kyn-ni) ‘day-accusative’

c. ok-t!˜ (*ok-tu˜) ‘of the arrow’

d. ÿØr-zip (*ÿØr-zyp) ‘having gone’

(38a) and (38b) show that the high vowel in the suffix agrees with the root vowel

in roundness, if the root vowel is [+high, round]. However, as seen in (38c) and

in (38d), the high vowel in the suffix is unrounded when the root vowel is round

but non-high.

As in Turkish, a round non-high vowel is not observed in suffixes even

when a root contains a round vowel.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9%!Korn (1969), however, uses the term ‘palatal harmony,’ rather than backness harmony in his description of Kachin Khakass.

! 192!

(39) No [-high] round vowels in suffixes (Korn 1969: 102)

a. pol-za (*pol-zo) ‘if he is’

b. ÿØr-gæn (*ÿØr-gØn) ‘who went’

c. kuzuk-ta (*kuzuk-to) in the nut’

d. kyn-gæ (*kyn-gØ) ‘to the day’

The spreading analysis in (40) shows that the restriction on the occurrence

of non-high round vowels is captured by the same mechanism as is assumed in

Turkish, namely, the markedness constraint (*o/Ø) dominating the spreading

constraint. I assume that in (40) and in subsequent tableaux, either the root

faithfulness constraint or the initial syllable faithfulness constraint preserves the

identity of the trigger. Thus, in (40), a candidate such as *[pal-za] is excluded by

these positional faithfulness constraints.

(40) No [-high, round] vowel in the suffix /pol-zo/ *o/Ø Spread [round] Id [round]

!a) pol-za $! [round]

b) pol-zo $! [round]

However, the ranking in (40) is not sufficient to rule out a candidate in

which the root vowel is [-high, round], and the suffix contains a high round

vowel. This is shown in (41); (41) shows the difference between Kachin Khakass

and Turkish with respect to the restriction on roundness harmony.

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(41) [+high, round] vowel in the suffix: /ok-tu˜/_[ok-t!˜] /ok-tu˜/ *o/Ø Spread [round] Id IO [round]

!a) ok-t!˜ $! [round]

b) ok-tu˜ $! [round]

In Turkish, the actual form would be (41b) since a high round vowel is observed

in suffixes even when the root vowel is non-high round. In Kachin Khakass, on

the other hand, the high vowel in suffixes can be round only when the root

vowel is [+high]. The markedness constraint *y/u (prohibiting high round

vowels) alone cannot be the solution, since high round vowels appear in suffixes

as in (38a) and (38b).

The solution is presented in (42) with the constraint in (41); in (42), an

additional markedness constraint, *y/u, is also included.

(42) [+high, round] vowel in the suffix: /ok-tu˜/_[ok-t!˜] /ok-tu˜/ *L-H

[round] *o/Ø Spread

[round] *y/u Id

[round]

$ a) ok-t!˜ $! [round]

b) ok-tu˜ $! [round]

In (42b), the [round] feature associated with a non-high vowel is also associated

with the following high vowel. *L-H [round] prohibits such a configuration. As

seen in (42), the ranking *L-H [round] >> Spread [round] predicts the pattern in

which a high vowel does not undergo harmony when the trigger is non-high.

! 194!

The analysis of the case with two [+high] vowels is presented in (43); (43)

shows that the ranking Spread [round] >> *y/u must be established.

(43) [+high, round] vowel in the suffix 2: /kuß-t!˜/_[kuß-tu˜] /kuß-t!˜/ *L-H

[round] *o/Ø Spread

[round] *y/u Ident IO

[round]

!a) kuß-tu˜ $! [round]

b) kuß-t!˜ $! [round]

Candidate (43a), in which the spreading of [round] is observed, obeys *L-H

[round]; since both of the round vowels in this candidate are [+high], this

constraint is silent with respect to this candidate. In (43), the spreading constraint

breaks the tie, and it selects the actual form over (43b), in which the spreading of

[round] is not observed. Thus, the spreading analysis in (42) shows that the

markedness constraint *L-H [round] is active in Kachin Khakass.

The following analyses show that ABC is able to account for the Kachin

Khakass patterns with the *L-H [round] constraint; (44) is the ABC analysis of the

case in which the high vowel in the suffix undergoes the harmony. In (44), the

following three constraints are included in the tableau: Corr [+hi] (that requires

that high vowels be in correspondence), Ident VV [round] (requiring that the

vowels in correspondence be identical with respect to roundness), and the

markedness constraint *u/y (prohibiting [+high] round vowels).

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(44) High vowel in the suffix becomes [round] /kuß-t!˜/ Corr [+hi] Ident VV [round] *u/y

!a) kuxß-tux˜ ** b) kuxß-t!x˜ *! * c) kuxß-t!˜ *! * In (44), candidate (44b) loses because of the output correspondent faithfulness

constraint; in this candidate, two vowels in correspondence are not identical with

respect to the roundness feature. (44c) loses because of Corr [+hi], since two high

vowels in the word are not in correspondence. (44) shows the ranking Corr [+hi],

Ident VV [round] >> *u/y.

(45) shows that the same ranking in (44) accounts for the case where a

high vowel does not undergo harmony when the trigger is non-high.

(45) High vowel in the suffix surfaces as unrounded /ok-tu˜/ Corr [+hi] Ident VV [round] *u/y

!a) oxk-t!˜ b) oxk-tux˜ *! c) ox-t!x˜ *! In candidate (45a), the [+high] unrounded vowel in the suffix is not in

correspondence while in (45b) and in (45c), the suffix vowel is in correspondence

with the vowel in the root. (45c) is excluded by the output correspondent identity

constraint for roundness, and (45b) loses because of the markedness constraint

prohibiting high round vowels.

However, the same problem arises in Kachin Khakass when backness

harmony is considered; in (46), candidate (46c) contains a suffix vowel which

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does not agree with the root vowel in backness. If (46c) is the competitor, then

we observed the same problem as observed in Yakut.

(46) High vowel in the suffix surfaces as unrounded /ok-tu˜/ Corr [+hi] Ident VV [round] *u/y

a) oxk-t!˜ b) oxk-tux˜ *! c) ox-ti˜ In (46), candidate (46b) loses because of the markedness constraint. However,

the remaining two candidates, (46a) and (46c), tie in this evaluation; they both

satisfy the correspondence constraint, the output correspondent identity

constraint, and the markedness constraint.

In Yakut, this problem is resolved by three additional constraints: Corr V-

V (requiring that all of the vowels in the word be in correspondence), Ident VV

[back] (requiring that vowels in correspondence be identical with regard to

backness), and *H-L [round]. I suggest the same solution for Kachin Khakass,

except I use the markedness constraint *L-H [round].

This solution is presented in (47). In (47), some additional candidates are

added to the evaluation. In (47), candidates (47c) and (47e) lose because of the

output correlation constraint (the suffix vowel is not in correspondence), and

(47d) loses because of the Ident VV [back] constraint. The markedness constraint

*L-H [round] is the tie breaker between (47a) and (47b), and this markedness

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constraint prefers the actual surface form (47a). (47) shows the ranking *L-H

[round] >> Ident VV [round].15

(47) High vowel in the suffix surfaces as unrounded /ok-tu˜/ Corr V-V Id VV

[back] *L-H

[round] Corr [+hi]

Id VV [round]

a) oxk-t!x˜ * b) oxk-tux˜ *! *! c) oxk-t!˜ *! d) oxk-tix˜ *! * e) oxk-ti˜ *!

The case study presented in this section shows that there are languages in

which *L-H [round] is active, and thus, the Uniformity [round] constraint can be

split without over-generating unattested roundness harmony patterns. This, in

turn, gives additional support to the claim that Kaun’s Uniformity constraint is

actually two constraints.16 This also gives additional support to the ABC and

spreading analyses of Yakut, in which the other half of the uniformity constraint

is necessary to correctly predict the attested harmony processes.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9&!One might ask whether the markedness constraint *y/u can replace *L-H [round] in (51). However, this cannot be the solution because, as seen in (46), the markedness constraint *y/u must be dominated by Ident VV [round]. 9.!Kaun (1995: 123) analyzes the restrictions on roundness harmony, as observed in languages such as Kachin Khakass, by the constraints, *o/Ø, Uniformity [round], and Extend [round] (the effect of which is the same as that of Spread [round]). Kaun suggests that the ranking *o/Ø, Uniformity [round] >> Extend [round] accounts for the restrictions that are observed in Kachin Khakass.

! 198!

CHAPTER VI ISSUES IN THE OT TREATMENT OF VOWEL HARMONY

Thus far, case studies of three different languages have been discussed. I

have demonstrated that both the feature linking approach and the ABC

approach are successful in accounting for the data from Pulaar ATR harmony, as

well as the backness/roundness harmony observed in Turkish and in Yakut. This

chapter provides a summary of the analyses that have been presented in this

thesis.

There are three purposes of this chapter: first, to provide a summary of

the discussions that have been presented thus far; second, to discuss the

remaining issues with regard to the OT treatment of vowel harmony; and finally,

to present a general conclusion for the thesis. The organization of this chapter is

as follows; a summary of the analyses is presented in Section 6.1. In Section 6.2,

two remaining issues with the constraint Spread are discussed. Section 6.3

contains a discussion of another harmony pathology, the ‘too many solutions

problem’ in OT, and a general conclusion for the thesis is presented in Section 6.4.

6.1 Summary

In Chapter 1, I have presented five approaches that have been proposed

to account for vowel harmony within the OT framework. However, as discussed

in Chapter 1, two of the approaches, feature alignment and local agreement,

have been eliminated for theoretical and empirical reasons. Thus, in this thesis,

three approaches, i) feature linking, ii) Span Theory, and iii) ABC, have been

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discussed; as seen in Chapter 2 (in the case study of Turkish), all three

approaches are applicable to vowel harmony, even though two of the

approaches, Span Theory and ABC, were originally proposed to account for

consonant harmony.

A summary of the analyses is presented in (1). As discussed in Chapter 4,

the directionality problem and the Sour Grapes problem can be resolved by a

single mechanism both in spreading and in ABC; that is, I suggested that these

two problems are related, and if one can be resolved (by one mechanism), the

other can be also resolved (by the same mechanism).

Table 12. Summary of the Analyses Directionality Sour Grapes Roundness and

backness harmony

Feature linking (spreading)

!Yes, with specified directionality in Spread (Ch4) - However, it requires the assumption of binary features

! Yes, with two separate Spread constraints (Ch2,5)

ABC !Yes, through lack of correspondence (Ch4)

!Yes, with *H-L [round] (Ch5)1

Span Theory !Yes "No, if features are assumed to be binary (Ch3)

!Yes, by assuming two spans for different features (Ch2)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

"!As far as roundness harmony is concerned, lack of correspondence accounts for the blocking effect in Yakut.

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One of the theoretical questions addressed in Chapters 3 and 4 is the issue

of the privativity or binarity of the feature [ATR]. As discussed in Chapter 3,

Span Theory crucially relies on the assumption of privative ATR; if binary ATR is

assumed, Span Theory fails to resolve the Sour Grapes problems. The

assumption of privative features cannot be maintained with all of the features

that participate in harmony cross-linguistically, and thus, I concluded that Span

Theory is not a viable theory to be used in accounting for vowel harmony.

Both spreading and ABC successfully account for the attested

directionality observed in Pulaar. However, these two approaches use different

mechanisms to account for the same data; in ABC, directionality is attributed to

the lack of correspondence (DLC) while in the spreading analysis, it is necessary

to specify directionality in the spreading constraint. These two approaches

resolve the Sour Grapes problem equally well, except that the spreading analysis

requires the assumption of binary [ATR] while for ABC, such an assumption is

unnecessary.

The case study of Yakut, which is presented in Chapter 5, shows that both

the spreading analysis and the ABC analysis require an additional markedness

constraint, *H-L [round]; without such a constraint, the ABC analysis encounters

a ranking paradox, and fails to account for both the roundness and backness

harmony observed in Yakut. The analysis with Spread also relies on this

markedness constraint; without this markedness constraint, a candidate that

exhibits an unattested combination of the round vowels wins.

! 201!

Therefore, to conclude, there are two viable approaches in OT to account

for harmony processes: spreading and ABC. However, as pointed out, spreading

constraints need some revision to fully account for the diverse vowel harmony

patterns attested cross-linguistically. Some discussion of the spreading

constraints is given in the next section.

6.2 On the Constraint Spread

As demonstrated in this thesis, one of the ways to approach vowel

harmony is to assume feature linking/spreading with the harmony constraint

Spread. However, there are two issues to be discussed about this constraint: the

directionality of harmony and the feature class node, [color].

The spreading constraint was originally proposed in Padgett (1997, 2002).

Padgett (2002) presents an analysis of Turkish vowel harmony using the

following spreading constraint.

(1) Spread (Color, PrWd) (Padgett 2002: 89) For all color features f in a prosodic word, if f is linked to any segment, it is linked to all segments.

As mentioned throughout this thesis, the constraint in (2) is fully satisfied when

all the segments (vowels) in a domain (such as a word) share the same feature

for [back] and [round] features, both of which are dominated by the class node,

color.

Padgett raises two points with regard to the spreading constraint. First, he

claims that spreading constraints are non-directional. (That is, it is not necessary

to specify the directionality of harmony in the spreading constraint.) Specifically,

! 202!

Padgett (2002) claims that directionality can be attributed to other phonological

phenomena, and thus, he assumes Spread in his analysis, rather than alignment

constraints, which are inherently directional. Second, Padgett (2002) suggests that

the spreading constraint in (2) targets a feature class/node, rather than individual

features, when it is used in languages such as Turkish and Yakut.

I have shown that the first point about directionality is not true in Pulaar,

and shown that it is necessary to specify the directionality of harmony. The

Pulaar case shows, however, that the directionality specified in the spreading

constraint determines the directionality of harmony when positional faithfulness

constraints are silent. In Chapter 4, I argued that it is necessary to specify

directionality in the spreading constraint itself to select the candidate with the

attested directionality.2

Padgett’s second point, that spreading constraints target feature classes

(when used in Turkish or Yakut), requires some explanation. The term [color]

(Odden 1991; Selkirk 1991) refers to a node/class in feature geometry; this class

contains two harmonic features, [back] and [round]. According to Padgett, these

two features are in (s0me kind of) structural relationship, since in many harmony

languages (for example, the majority of the Turkic languages, including Turkish

and Yakut), backness and roundness harmony occur together (cf. Archangeli !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

#!Sasa (2004) also points out that the analysis of Kinande dominant-recessive ATR harmony also requires Spread [+ATR]-L; the leftward directionality in Kinande cannot be attributed to root faithfulness since the vowel(s) in roots undergo harmony (underlying [-ATR] vowels in the root become [+ATR] when there is a [+ATR] vowel in a suffix).

! 203!

1985). Padgett further suggests, provided this fact, that a better analysis results if

a harmony constraint targets a feature class (more specifically, the class node

[color]) rather than each individual feature, with respect to simplicity and

naturalness. (That is, a simpler rule or constraint corresponds to more natural (or

more common) phenomena.) In other words, Padgett (2002) claims that the

analysis with Spread [color] offers a better (simpler) analysis than the analysis

with two separate spreading constraints in accounting for a language with

backness and roundness harmony. One might ask, however, how Spread (color)

can achieve the pattern observed in Turkish or in Yakut (that is, the pattern in

which all the vowels in a word participate in backness harmony, but some

vowels do not participate in roundness harmony); as stated, Spread (Color) is

satisfied only when all the vowels agree both in backness and roundness.

Padgett suggests that such a pattern can be accounted for as partial class

behavior through the gradient assessment of the candidates by the spreading

constraint.

To illustrate this, the analysis of Yakut roundness/backness harmony with

(1) is presented in (2). In (2), I use Padgett’s convention of using two different

brackets to show feature linking, rather than using association lines; [ ]B and ( )R

indicate that the segments in these brackets share the same backness feature and

roundness feature, respectively.

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(2) Yakut roundness/backness harmony with Spread [color] /tynnyk-ler/ *H-L [round] Spread [color] Ident [color]

!a) [(tynnyk)R-ler]B * b) [(tynnyk-lØr)R]B *! * c) [(tynnyk)R]B[-lar]B **! * Candidate (2b) completely satisfies Spread [color], since all the vowels

(segments) share the same [round] and [back] features.3 However, this candidate

is excluded by *H-L [round]. The candidates in (2a) and (2c) satisfy this

markedness constraint, so in (2), Spread [color] is the tie-breaker. Under this

spreading constraint, candidate (2a) is better than (2c); candidate (2a) incurs one

violation for the spreading constraint because the [round] feature is not linked to

the suffix vowel, but the [-back] feature is shared by all of the vowels. (2c), on the

other hand, incurs two violations for the vowel in the suffix; neither the [round]

feature nor the [-back] feature is linked to the vowel in the suffix, which gives

rise to two violations for Spread [color].

Thus, the same results are achieved by assuming Spread [color], rather

than assuming two separate spreading constraints. However, the use of Spread

[color] hinges on the assumption of a different organization of the features:

namely, the feature class, color.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

$!I follow Padgett in counting the violation(s) of the spreading constraint; that is, “for simplicity, IDENT and SPREAD violations are counted only with respect to vowels” (Padgett 2002: 91).

! 205!

6.3 Harmony Pathology Revisited

In chapters 3 and 4, I discussed one of the pathologies, Sour Grapes, and in

Chapter 4, I demonstrated how the analysis with spreading resolves this

problem. According to Wilson (2006), however, Sour Grapes is not the only

pathology. Another pathological case pointed out by Wilson is the so-called ‘too

many solutions problem’; in short, there are multiple ways to satisfy a certain

constraint, and depending on the ranking of the constraints, unwanted results

cannot be blocked.

To see what the problem is, let us assume the ranking permutation of Max

(“No deletion”) and (some of) the constraints that were used in Chapter 5 to

account for Yakut roundness harmony. In (3), I assume the same ranking of the

constraints as is assumed for Yakut, and Max dominates all other constraints. (In

(3), the blank column means that Max dominates all other constraints, but it does

not necessarily mean that Max is ranked right above the positional faithfulness

constraint.)

(3) The effect of Max /tynnyk-lØr/ Max Id !1 [rd] *H-L [rd] Spread [rd] Id [rd]

! a) tynnyk-ler * * b) tynnyk-lØr *! c) tinnik-ler *! *** d) tynnyk *!** (3) shows that there are three possible ways to satisfy Spread [round]; spreading

the [round] feature to the suffix vowel as in (3b) (even though in (3), such a

candidate is eliminated by the markedness constraint), deleting the [round]

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feature from the output as in (3c), or deleting the suffix (vowel) as in (3d). These

unattested ways to satisfy Spread [round] are blocked either by the markedness

constraint, which excludes (3b), by the positional faithfulness constraint, which

excludes (3c), or by Max, which excludes (3d).

However, one of the core assumptions of the OT grammar is ranking

permutation. For example, as seen in Chapter 2 and Chapter 5, the different

rankings between the markedness constraint *o/Ø (prohibiting non-high round

vowels) and the spreading constraint explain the difference between Yakut and

Turkish in roundness harmony. (4) presents another ranking permutation, in

which Max is dominated by all other constraints. As a result, candidate (4d), the

deletion candidate, is selected as optimal. (In (4) and in subsequent tableaux, the

blank column means that Max is dominated by all other constraints, but it is not

ranked right below Ident [round].)

(4) Too many solutions 1 /tynnyk-lØr/ Id !1 [rd] *H-L [rd] Spread [rd] Ident [rd] Max

a) tynnyk-ler *! * b) tynnyk-lØr *! c) tinnik-ler *! *** ! d) tynnyk *** Candidate (4c) still loses because of the positional faithfulness constraint, and (4b)

loses because of the markedness constraint. The spreading constraint is the tie-

breaker in (4), and it favors (4d), the deletion candidate, over candidate (4a).

Here, the problem is not that a different candidate is selected by the different

ranking, since such a result is predicted in the OT grammar. The real problem is,

! 207!

however, that the ranking in (4) predicts an unattested pattern, where complete

spreading is achieved by deleting segments.

The analysis in (5) presents another problem; in (5), the same ranking as in

(4) is assumed, but the input is different.

! a) o©o-nu b) o©o-n! *! * c) a©a-n! *! *** d) o©o *!* In (5), Max is dominated by other constraints as in (4), but a different result is

predicted. Unlike (4), both (5a), the spreading candidate, and (5d), the deletion

candidate, satisfy the spreading constraint. Max is the tie-breaker in (5), and this

faithfulness constraint favors (5a) over the deletion candidate.

The problem presented thus far is summarized as follows: the grammar in

(4) and (5) exhibits a pattern in which i) roundness harmony is complete when all

the vowels can participate in harmony (as in (5)), but ii) if there is a vowel that

cannot participate in harmony, as in (4), the vowel is deleted to achieve complete

harmony. As stated, deletion is not an attested pattern in harmony to achieve

complete harmony. That is, this implies that the grammar established in this

thesis would collapse because such a system would over-generate patterns which

are not attested in any harmony language at all.

As seen in (6) and (7), ABC cannot solve this problem, either; in (6) and in

(7), two of the ABC constraints, Corr V-V (requiring vowels to be in

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correspondence), and Ident VV [round] (requiring correspondent vowels to be

identical with respect to roundness) are included along with the constraints that

were assumed in (4) and (5).

(6) Deletion with a blocker /tynnyk-lØr/ Id !1 [rd] *H-L [rd] Corr V-V Id VV [rd] Max

a) tyxnnyxk-ler *! b) tyxnnyxk-lexr *! c) tyxnnyxk-lØx r *! d) tixnnixk-lexr *! ! e) tyxnnyxk *** (7) No deletion without a blocker /o©o-nu/ Id !1 [rd] *H-L [rd] Corr V-V Id VV [rd] Max

! a) ox©ox-nux b) ox©ox-n! c) ax©ax-n!x *! d) ox©ox *!* (6) shows that the deletion candidate (6e) is selected as optimal in ABC as well.

The difference between (6a) and (6b) is that the suffix vowel is not in

correspondence in (6a) while in (6b), all of the vowels are in correspondence. (6a)

and (6b) are excluded because of the correlation constraint and the

correspondent identity constraint, respectively. (6c) violates *H-L [round] and

(6d) violates the initial syllable faithfulness constraint, and as a result, the deletion

candidate is selected as optimal.

In (7), on the other hand, the deletion candidate (7d) loses because of Max.

In (7a), all of the vowels are in correspondence, and they are all identical in

roundness. Thus, (6) and (7) show that the same prediction results even in the

ABC analysis; no deletion is observed when there are no blockers. If there is a

! 209!

blocker, complete harmony is achieved by deletion. Thus, ABC also fails to block

the unattested/unwanted pattern when the effects of Max are not visible.

There are two important observations to be made here, however. First,

the ‘too many solutions problem’ is not limited to vowel harmony, and second, a

variety of solutions to this problem have been proposed. As noted, the ‘too

many solutions’ problem arises in accounting for other phonological

phenomena, such as voice assimilation. Cross-linguistically, a voice assimilation

process in which a pair of adjacent obstruents agrees in voicing is commonly

observed. Russian, for example, is one such language; in Russian, in a pair of

adjacent obstruents, the rightmost one triggers regressive voice assimilation (for

example, pro[s’]it’ ‘to beg’ vs. pro[z’b]a ‘request’ (Petrova et al. 2006: 5)). The

same problem arises in such a voice assimilation case, as well, if Max is

dominated by other constraints; that is, it is not possible to block an unattested

pattern in which the requirement of voice assimilation is satisfied by deletion

rather than by making adjacent obstruents agree in voicing, if the effects of Max

are invisible. This illustrated in (8).

(8) Too many solutions in voice assimilation (cf. Petrova et al. 2006: 6) pro/s’b/a Agree (lar) Id preson [voi] *voi Max

"a) pro[z’b]a *!* b) pro[s’b]a *! * c) pro[s’p]a *! #d) pro[s’]a * In (8), in addition to Max, the following three constraints from Petrova et al.

(2006) are assumed: Agree (lar) (“Obstruents in a cluster must agree in laryngeal

! 210!

specifications”), Id presonorant [voi] (“An obstruent in presonorant position

must be faithful to the input specification for voice”), and *voi (“Voiced

obstruents are prohibited”). In (8), (8b) loses because of the agreement

constraint, and the positional faithfulness constraint excludes candidate (8c).

As stated, the actual form in Russian is (8a). However, if the effects of Max

are not visible (that is, if Max is low-ranked), the actual form loses to the deletion

candidate (8d). The problem illustrated in (8) is that, as in vowel harmony,

deletion is not attested to achieve voice assimilation. In other words, if this

ranking permutation is permitted (in fact, no standard OT assumptions prohibit

such a ranking permutation), no mechanism can block such an unattested

pattern from surfacing or being selected in voice assimilation, either.

Thus, I suggest that the ‘too many solutions’ problem is, in fact, a problem

with the theory as a whole, and is not limited to vowel harmony. If we cannot

remedy this problem, the whole theory of Optimality Theory will be in jeopardy,

since OT fails to predict the attested patterns, and only the attested patterns, in

accounting for a common phonological phenomenon as harmony or

assimilation.

There are several approaches that have been proposed as a solution to

this problem, however. These solutions include Targeted Constraints (Bakovic

and Wilson 2004), the Turbidity (Goldrick 2001) analysis as proposed by Finley

(2008), and Harmonic Serialism, proposed by McCarthy (2009). All of these

approaches involve modifications of the theory; targeted constraints specify the

! 211!

methods of repair for voice assimilation (Bakovic and Wilson 2004), while

Turbidity assumes enriched output representations. The rest of this section

describes the one of the solutions, Harmonic Serialism.4

Harmonic Serialism is a version of OT in which GEN is allowed to make

one change at a time. The evaluation of the candidates is referred to as a pass

through GEN and EVAL, and the evaluations are conducted serially until the

optimal candidate converges on the input.

The analysis in (9) is the implementation of McCarthy’s proposal in Yakut

roundness harmony with the harmony constraint Spread.

(9) Serialism analysis: first pass /tynnyk-lØr/ Id !1 [rd] *H-L [rd] Spread [rd] Ident [rd] Max

!a) tynnyk-ler * * b) tynnyk-lØr *! c) tinnyk-ler *! * ** One might ask why a deletion candidate is not included as a possible

candidate in (9). McCarthy claims that GEN will not create a deletion candidate

[tynnyk], since deletion of a segment involves multiple changes of the input.

According to McCarthy (2008, 2009), deletion is viewed as ‘a gradual process of

attrition.’ For example, the deletion of [Ø] involves the deletion of the feature

[round], the deletion of the feature [-back], the deletion of the feature [-high],

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

%!The full analysis with Turbidity (with two different kinds of Max, operating in two different levels of representations) is presented in Finley (2008). As discussed in Chapter 1, there are existing critiques of (the existence) of targeted constraints in the literature, and thus, I do not present a detailed discussion of the solution with targeted constraints in this section.

! 212!

and so on. In Harmonic Serialism, only the deletion of a single feature is allowed

because GEN is limited to making one change at a time (or in a single pass).

Thus, in (9), GEN creates a candidate [tynnyk-lØr] (no change), [tynnyk-ler] (one

change: the deletion of [round]), or [tinnyk-lØr] (changing the roundness feature

of the vowel in the first syllable), but not [tynnyk], which involves the deletion of

multiple features.

In (10), the optimal form does not converge with the input (that is,

evaluations are performed until the input and the winning candidate become

identical). Thus, another evaluation is performed with the optimal candidate of

the first pass being the input of the second pass.5

(10) Serialism analysis: second pass /tynnyk-ler/ Id !1 [rd] *H-L [rd] Spread [rd] Ident [rd] Max

!a) tynnyk-ler * b) tynnyk-lØr *! c) tinnyk-ler *! * * In (10), the winner of the first pass is the input, and the optimal candidate

converges with the input. Therefore, the ‘derivation’ is completed, that is, a third

pass is unnecessary; even if the third pass were to be examined, the result would

be the same. Both in (9) and in (10), a deletion candidate cannot be a competitor,

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&!In this sense, Harmonic Serialism is similar to Serial OT or Derivational OT (cf. Rubach 1997, 2003). However, the crucial difference is that constraint re-ranking is not part of the mechanism in Harmonic Serialism.

! 213!

since GEN does not create such a candidate in either pass, and there is no need

for any more passes.6

As seen in (9) and in (10), Harmonic Serialism, along with other two

proposed solutions, can resolve one of the pathologies, the too many solutions

problem. The solutions mentioned in this section (targeted constraints and

Turbidity, along with Harmonic Serialism) all require some modification to the

theory. In other words, there are some controversial issues that arise with all of

these proposals, and consequently, no general consensus has thus far been

achieved as to the solution to the problem. Nonetheless, let me point out that

new developments of the theory have been made so that the new proposals

save OT from jeopardy. Therefore, I conclude that OT is a viable theory to

account for vowel harmony even though the theory will need some further

development.

6.4 Conclusion

There are two main questions that have been addressed in this thesis: first,

can OT handle vowel harmony, and second, if so, then what is the mechanism

that can offer a unified analysis of the diverse patterns in vowel harmony? The

answer to the first question is that it is possible to analyze vowel harmony in OT.

As demonstrated, there are two possible approaches to vowel harmony within

the OT framework: feature spreading and ABC. Therefore, we can conclude that !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

'!One might ask, then, what if deletion actually takes place? The answer will be that more passes are examined until the deletion candidate is selected as optimal, and converges with the input.

! 214!

OT can handle at least the vowel harmony patterns presented here, even though

both spreading and ABC requires some modifications of their theoretical

assumptions, or some additional mechanisms.

One might ask, then, which approach, spreading or ABC, presents the

more comprehensive accounts of vowel harmony? The answer is that both of

them are valid approaches to vowel harmony. In other words, it is not

straightforward to determine which approach is superior to the other; as we

have seen, in some cases (for example, in Pulaar ATR harmony), the ABC

approach is better in that, unlike the spreading approach, it does not require any

additional mechanisms (such as specifying directionality in spreading), or any

particular assumptions (such as the assumption of binary [ATR], which the

spreading analysis crucially relies upon). In Yakut harmony, on the other hand, it

is true that both spreading and ABC are capable of accounting for the attested

data, but no factor in Yakut favors either one of these approaches (that is, both

of these approaches require *H-L [round] to fully account for the data).

In this thesis, I have considered diverse vowel harmony systems (both

roundness and backness harmony in two languages, ATR harmony, and

directionality), but there are still other types of harmony that must be

considered. Therefore, further comparison between the spreading analysis and

the ABC analysis will determine how well these two alternative approaches

handle other cases of vowel harmony.

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