1

Gradient Grammaticality of theIndefinite Implicit Object Construction

in English

Tamara Nicol Medina

IRCS, University of Pennsylvania

Collaborators:Barbara Landau 1, Géraldine Legendre 1, Paul Smolensky 1, Philip Resnik 2

1 Johns Hopkins University, Department of Cognitive Science 2 University of Maryland, Department of Linguistics, Department of Computer Science

2

The (Indefinite) Implicit Object Construction (in English)

John is eatingJohn is reading

• Verb selects for an object, but none is overtly specified.

• Interpretation is of an indefinite and non-specific object.

(something / some food). (something / written material).

* John is reading (War and Peace).

• Grammaticality varies across verbs.* John is pushing.* John is opening.

Verb Semantic SelectivityAspect (Telicity, Perfectivity)

3

Overview1. Factors that Affect Grammaticality of an Implicit

Object• Verb Semantic Selectivity• Aspectual Properties (Telicity, Perfectivity)

2. Grammaticality Judgment Study

3. Linguistic Analysis (Optimality Theory)

4. Estimation of Constraint Ranking Probabilities

5. Implications for Acquisition

4

Verb Semantic Selectivity• The omitted object tends to be

recoverable from the verb.John is eating (some food) / drinking (a beverage) / singing

(a song).• Verbs that select for a wide variety of

semantic complements, and therefore there is no one recoverable interpretation, tend to resist implicit objects.John is bringing *(something) / making *(something) /

hanging *(something).Indefinite implicit objects are allowed to the extent

that they are recoverable.

5

Selectional Preference Strength (SPS) (Resnik, 1996)

Don’t push your brother.Move that chair.Do you want an apple?

“like”

Tony likes that girl.I don’t like this couch.I really like bananas.

People Furniture FoodsPeople Furniture Foods

“eat”

Eat your lunch.He’s eating cereal.She always eats avocados.

People Furniture Foods

cvc

vcvSPS i

cii Pr

PrlogPr

An information-theoretic model of verbs’ strength of semantic preferences. Calculates the strength of a verb’s selection for the semantic argument classes from which its complements (or objects) are drawn.

For all argument classes (c), PRIOR, Pr(c) – the overall distribution of argument classes POSTERIOR, Pr(c|vi) – the distribution of argument classes, given a particular verbThe greater the difference between Pr(c) and Pr(c|vi), the higher SPS will be.(Argument classes were those listed in WordNet.)

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Selectional Preference Strength (SPS) (Resnik, 1996)

• SPS correlated with experimental measures of recoverability and ease of inference (Resnik, 1996).

– SPS corresponds to what people know about verbs’ selectional preferences.

• SPS correlated with rate of object omission in Brown corpus of American English (adult written English) (Resnik, 1996).

– SPS directly affects syntax.

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SPS and Implicit Objects

Relative SPS is correlated with the relative frequency of an implicit object.Brown corpus of American English (Francis and Kučera, 1982 )

0%10%20%30%40%50%60%70%80%90%

100%

pour

drin

kpa

cksi

ngst

eal

eat

hang

wea

rop

enpu

sh say

pull

like

writ

epl

ay hit

catc

hex

pla

read

wat

cdo

hear call

wan

tsh

owbr

ing

put

see

find

take ge

tgi

vem

ake

Verb

% Implicit Objects

4.80

0.72

SPS % Implicit Objects

SPS

r = 0.48, p < 0.05

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Verb Semantic Selectivity• High SPS is a necessary, but not sufficient

condition on object omissibility.– Some verbs with high SPS do not occur with

implicit objects, e.g., hang.– Not an inviolable rule.

• SPS is a continuous measure. How to incorporate this into a formal grammar?

– As a statistical component to the grammar.

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TELICExistence of an inherent endpoint.

ATELICNo inherent endpoint.

“The ship sank.”

Telicity (Lexical Aspect)

“The ship floated.”

A direct object serves to measure out the event.

[+ Telic]“Kim is eating an apple.” incremental THEME(Once the apple is gone, the event is over.)

[+ Atelic]“Kim is eating.”

[+Telic]“Kim arrived.”

Requires an overt object.

Does not require an overt object.

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Telicity (Lexical Aspect)

• Atelicity is a necessary, but not sufficient condition on object omissibility.

– Some atelic verbs do not occur with implicit objects, e.g., push, pull.

– Not an inviolable rule.

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Perfectivity (Grammatical Aspect)

[+ Perfective]“Kim had written */?(something).”

[+ Imperfective]“Kim was writing.”

Requires an overt object.

Does not require an overt object.

PERFECTIVEPerspective of event endpoint.

IMPERFECTIVEPerspective of ongoing event.

have + past participle “The ship has sunk.”

be + “-ing”“The ship is sinking.”

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Perfectivity (Grammatical Aspect)

• Imperfectivity is a necessary, but not sufficient condition on object omissibility.

– Perfectivity doesn’t render a sentence with an implicit object completely ungrammatical, while Imperfectivity doesn’t necessarily make it grammatical.

•Michelle had written ?(something). PERFECTIVE•Michelle was hearing *(something). IMPERFECTIVE

– Not an inviolable rule.

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Putting the Puzzle Together

No single factor completely distinguishes verbs that omit objects from verbs that do not.

– SPS continuous measure which is related to the relative frequency of an implicit object.

– Some Telic verbs do allow implicit objects, while some Atelic verbs do not.

• Michelle packed. TELIC• Michelle wanted *(something).ATELIC

– Perfectivity doesn’t render a sentence with an implicit object completely ungrammatical, while Imperfectivity doesn’t necessarily make it grammatical.

• Michelle had written ?(something). PERFECTIVE• Michelle was hearing *(something). IMPERFECTIVE

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Method

Grammaticality Judgment Study

Subjects 15 monolingual adult native speakers of English

Stimuli 30 verbs, 160 sentences

SPS (Resnik, 1996)TelicityPerfectivity

Verb-Argument Structure

Sentence Type Direct Object Example Sentence

Two-Argument Verbs (n = 30)

Target Implicit Objects Michael had brought.Michael was bringing.

Control Overt Objects Sarah had brought a gift.Sarah was bringing a gift.

One-Argument Verbs (n = 10) Filler

No Objects Emma had slept.Emma was sleeping.

Overt Objects Andrew had slept a blanket.Andrew was sleeping a blanket.

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Results

Grammaticality Judgment Study

1

2

3

4

5

put

get

like

mak

ebr

ing find

want

wear

take say

open

show giv

eca

tch

hang hit see

pour pull

hear

push

drink

watc

hwr

ite call

read sing eat

play

pack

Verb

Aver

age

Gram

mat

icali

ty J

udgm

ent

.

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Verb Semantic Selectivity (SPS)

Grammaticality Judgment Study

1

2

3

4

5

0.50 1.50 2.50 3.50 4.50

Selectivity

Aver

age G

ram

mati

calit

y Jud

gmen

t

.

r = 0.66, p < 0.05

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Telicity

Grammaticality Judgment Study

F = 11.357, p < 0.05

1

2

3

4

5

Telic Atelic

Aver

age G

ram

mati

calit

y Jud

gmen

t

.

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Perfectivity

Grammaticality Judgment Study

F = 3.63, p = 0.06

1

2

3

4

5

Perfective Imperfective

Aver

age G

ram

mati

calit

y Jud

gmen

t

.

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Summary of Findings

Grammaticality Judgment Study

• Gradient across verbs.Effects of Verb Semantic Selectivity (SPS), Telicity, and Perfectivity.

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Optimality Theory(Prince and Smolensky, 1993/2004)

An Optimality Theoretic Analysis

• Formulate conditions as violable constraints, not inviolable rules.

• Take advantage of the component in OT called "CON", in which constraints are ranked with respect to one another.

– It is the evaluation of the output candidates against the set of ranked constraints that determines the optimal output.

– This will allow some constraints to have a greater effect than others.

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Optimality Theory(Prince and Smolensky, 1993/2004)

An Optimality Theoretic Analysis

• A strict ranking hierarchy (as in standard OT) will be shown to be too strong.

• Take insights from partial ranking approaches.• Furthermore, will incorporate a statistical

component to the ranking of constraints, which will allow for the derivation of GRADIENT grammaticality.

However…

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OT Framework

catch (x,y)x = David, y = unspecified SPS=2.47Telic, PerfectiveDavid had caught.

David had caught something.

* INTERNAL ARGUMENT (* INT ARG) The output must not contain an overt internal argument (direct object).

* INT ARG

FAITHFULNESS TO ARGUMENT STRUCTURE (FAITH ARG) An internal argument in the input must be realized by an overt object.

FAITH ARG

* INT ARG

FAITH ARG

TELIC ENDPOINT (TELIC END) The internal argument must be overtly realized in the output, given Telic aspect.

PERFECTIVE CODA (PERF CODA) The internal argument must be overtly realized in the output, given Perfective aspect.

TELIC END

PERF CODA

eat (x,y)x = David, y = unspecified SPS=3.51Atelic, ImperfectiveDavid was eating.

David was eating something.

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Ranking of Constraints

catch (x,y)x = David, y = unspecified SPS=2.47Telic, PerfectiveDavid had caught.

David had caught something.

* INT ARG

FAITH ARG

TELIC END

PERF CODA

* INT ARG

FAITH ARG

p(*I » F) p(*I » T) p(*I » P)

* ARG OF HIGH

SPS VERB

p(*I » F) x p(*I » T) x p(*I » P) = p( *I » {F, T, P} )

1min

minmax

11

SPSSPSSPSSPS ip(*I » F) =

2min

minmax

22

SPSSPSSPSSPS i

3min

minmax

33

SPSSPSSPSSPS i

p(*I » T) =

p(*I » P) =

p(*I » F) x p(*I » T) x 1- [ p(*I » P) ] = p( P » *I » {F, T} )

Problems• How to find perfect cut off value?• Strictly ranked constraints won’t give rise to gradient grammaticality.

What about SPS?What is needed is a flexible ranking of constraints.• Partial Ranking: One or more constraints “floats” among other

ranked constraints.• Current Approach: NO ranked constraints, only a floating constraint.

If * INT ARG is highest ranked, then the implicit object is optimal.If FAITH ARG is highest ranked, then the overt object is optimal.• Similar for TELIC END and PERF CODA.

Linear Function:As SPS increases, so does the relative ranking of * INT ARG.

Joint Probabilities = Set of Rankings (a partial ranking of constraints)

For each pairwise probability, such as p(*I » F), given a total probability of 1, there is the opposite probability, 1 - p(*I » F).

Incorporating these gives rise to different partial rankings with different optimal outputs.

catch (x,y)x = David, y = unspecified SPS=2.47Telic, Imperfective

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Total Set of Possible Partial Rankings

Telic Perfective

Telic Imperfective

Atelic Perfective

Atelic Imperfective

*I » {F, T, P} implicit implicit implicit implicit

P » *I » {F, T} overt implicit overt implicit

T » *I » {F, P} overt overt implicit implicit

{T, P} » *I » F overt overt overt implicit

F » *I » {T, P} overt overt overt overt

{F, T} » *I » P overt overt overt overt

{F, P} » *I » T overt overt overt overt

{F, T, P} » *I overt overt overt overt

12.5%

12.5%12.5%

12.5%

12.5%

12.5%

12.5%12.5%

The various combinations of pairwise rankings can be captured by 8 partial rankings.

– Give rise to OVERT or IMPLICIT object output depending on the aspectual properties of the input.

12.5% 25% 25% 50%NON-equiprobability p(*I » F) = 0.75 p(*I » T) = 0.85 p(*I » P) = 0.55

35.1% 63.8% 41.2% 75%

35.1%28.7% 6.2% 5.1%11.7% 2.1% 9.6% 1.7%

Probability of Implicit Object

Calculate the probability of an IMPLICIT object output as the total proportion of rankings that give rise to it.

– This is equivalent to the grammaticality of an implicit object output. – If equiprobable: 1/8 = 12.5%.

Calculate the probability of an IMPLICIT object output as the total proportion of rankings that give rise to it.

– This is equivalent to the grammaticality of an implicit object output.– If equiprobable: 1/8 = 12.5%.– But they are not equiprobable, since they depend on the joint pairwise

ranking probabilities that compose them, and these are tied to SPS.

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Summary of OT Analysis

The grammaticality of an implicit object for a particular verb…

is equivalent to the probability of the implicit object output for that input,

which… depends upon the probabilities of each of the possible partial rankings,

which… depends on the probabilities of *I » F, *I » T, and *I » P,

which… are a function of SPS.

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Finding the Probabilities

So what are the pairwise probabilities of *I » F, *I » T, and *I » P in English?

Can we even find probabilities that would work for all verbs?

Use grammaticality judgment data to estimate the probabilities.

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Estimation of the Constraint Rankings for English

= p(*I » F) p(*I » T) p(*I » P)

p(implicit)Telic Perfective = p(*I » {F, T, P})

= grammaticality judgment

111 72.096.072.080.4

222 72.096.072.080.4

333 72.096.072.080.4

1.93

=

x

x

.23

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Estimated Probability Functions for English

p(*I » F) p(*I » T) p(*I » P)

0.00

0.20

0.40

0.60

0.80

1.00

0.72 4.80

SPS

p (*

INT

ARG

>>

TELI

C EN

D)

.

0.00

0.20

0.40

0.60

0.80

1.00

0.72 4.80

SPS

p (*

INT

ARG

>>

PERF

CO

DA)

.

0.00

0.20

0.40

0.60

0.80

1.00

0.72 4.80

SPS

p (*

INT

ARG

>>

FAIT

H AR

G)

.

• Taking the grammaticality judgments as a direct reflection of the probabilities of an implicit object being generated by the grammar.

• Estimated what the pairwise rankings must be in order to produce these results.

• The probability of * INT ARG ranked above each of the other three constraints increased with SPS.

• Steepest function for the relative ranking of * INT ARG with TELIC END.

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Overall Predicted Grammaticality of An Implicit Object

0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5

SPS

Prob

abilit

y of Im

plici

t Obj

ect O

utpu

t

.

Telic Perfective

Telic Imperfective

Atelic Perfective

Atelic Imperfective

• Best for Atelic Imperfective, worst for Telic Perfective.• Increase as a function of SPS, but differentially depending on aspect

type.- Telic Imperfectives show greatest effect of SPS.

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Correlations between Judgments and Model

Telic Perfectiver = 0.84, p < 0.05

Telic Imperfectiver = 0.88, p < 0.05

1.00

2.00

3.00

4.00

5.00

0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7

SPS

Gra

mm

atica

lity o

f Im

plicit

Obje

ct

.

.

ModelJudgments

1.00

2.00

3.00

4.00

5.00

0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7

SPS

Gra

mm

atica

lity o

f Im

plicit

Obje

ct

.

.

ModelJudgments

Atelic Imperfectiver = -0.09, p > 0.05

1.00

2.00

3.00

4.00

5.00

0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7

SPS

Gra

mm

atica

lity o

f Im

plicit

Obje

ct

.

.

ModelJudgments

Atelic Perfectiver = 0.26, p > 0.05

1.00

2.00

3.00

4.00

5.00

0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7

SPS

Gra

mm

atica

lity o

f Im

plicit

Obje

ct

.

.

ModelJudgments

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What is the nature of the indefinite implicit object construction in the adult grammar?

OT Analysis

• The grammaticality of an implicit object across verbs is– Gradient.– Reduced in accordance with SPS, Telicity, and Perfectivity.

• For any verb, if you know SPS, Telicity, and Perfectivity, then the grammar generates a relative grammaticality for the implicit object output with that verb.

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Linguistic Analysis

Turning to acquisition, we can now ask what the learner’s task must involve:• Find p(*I » F), p(*I » T), and p(*I » P).

How?• The model’s values were estimated from grammaticality judgments.• But children don’t “hear” grammaticality judgments!

- Occurrence of implicit indefinite objects: increase ranking of * INT ARG.- Occurrence of overt indefinite objects: reduce ranking of * INT ARG.

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Implications for Acquisition

For example,• Assign a grammaticality of 0 for any verb that never occurs with an implicit

object.• Assign a grammaticality of 1 for any verb that occurs with an implicit object at

least 20% of the time.• Assign a grammaticality of 0.50 for any verb that occurs with an implicit

object infrequently: 0 – 20% of the time.

0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5

SPS

Prob

abilit

y of Im

plici

t Obj

ect O

utpu

t

.

Telic Perfective

Telic Imperfective

Atelic Perfective

Atelic Imperfective

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Conclusions

• The grammaticality of the indefinite implicit object construction is– Gradient, as shown in the Grammaticality Judgment Study.– Determined by a combination of factors, including Verb Semantic

Selectivity (SPS), Telicity, and Perfectivity.• It is possible to derive gradient grammaticality, by allowing

constraints to "float" and assessing grammaticality over the total set of possible rankings.

• Estimation of the constraint ranking probabilities for English showed that it is, in fact, possible to find rankings that capture the phenomenon with low error.

• Raises interesting questions for acquisition:– What is the state of the child's early grammar?– How does the learner adjust her grammar in accordance with what

she hears in the child-directed input (not grammaticality judgments) in order to arrive at a grammar that displays gradient judgments?