Knowledge Summarizationusing Decision Logic

Case Study: Polish Gender Theory

Knowledge Summarizationusing Decision Logic

Case Study: Polish Gender Theory

Paweł STACEWICZ & André WLODARCZYK

ABOUT DECISION LOGIC

Decision Logic (DL) was proposed by Zdzisław Pawlak as a formal tool, that connects his theory of rough sets (RST) with concept of reasoning in knowledge representation systems (KRS).[Pawlak Z., 1991]

The main concern od DL is induction (not deduction), i.e. this tool is best suited for discovering dependencies in data and reduction of knowledge.

Atomic formulas of DL has the form (a,v) or av, meaning that attribute a of object under observation has value v.Compound formulas of DL are built of atomic formulas and common logic connectives, like „”, „” and „→”.

From inductive point of view the most important formulas are decision rules, which takes the form p1p2… pn →q (where pi and q are atomic formulas).Set of decision rules is called decision alghoritm.

DECISION TABLESDecision tables are the most clear representation of decision rules sets (i.e. decision algorithms). Each row of such a table corresponds to one rule and each column corresponds to one attribute of objects under observation.

Set of columns is divided into two categories: condition columns, which corresponds to attributes in predecessors of rules, and decision columns, which corresponds to attributes in successors of rules.

Sample decision table Corresponding set of rules(decision algorithm)

a b c d

x1 1 0 1 0

x2 1 2 0 0

x3 0 1 1 1

x4 1 1 1 1

r1: a1b0c1→d0

r2: a1b2c0→d0

r3: a0b1c1→d1

r4: a1b1c1→d1

DECISION LOGIC – SOME EXAMPLESDecision table (model)

a b c d

x1 1 0 1 0

x2 1 2 0 0

x3 0 1 1 1

x4 1 1 1 1

Sample formulas

a1, b0, d0 (atomic formulas) a0b1, a1b2c1 (conjunctions) a0b1, a1b2c1 (alternatives) a1b1c1→d1 (implication, i.e. decision rule) a1(a0c1)(b0c0)→d0 (disjunctive decision rule)

Meanings (extensions) of formulas

| a1| = {x1,x2}, | b0 | = {x1}| a0b1| = {x3}, | a1b2c1 | = {x1,x2,x3,x4}| a1b1c1→d1 | = {x1,x2,x3,x4}

Note: Two last formulas are satisfied by all objects xi and from this reason are said to be true in model (i.e. in respect to observations collected in decision table).

SIMPLIFICATION OF KNOWLEDGE

IDEA

One of the most interesting applications of DL is simplification of given rule sets in such a manner that final set of rules has the same „decision-making strength” as initial set.

The main goal of simplification is to maximally reduce number of rules and number of components in predecessors of rules.

SIMPLIFICATION OF KNOWLEDGE PROCEDURE

Step 1: ELIMINATION OF SUPERFLUOUS ATTRIBUTES

(Deletion of decision table columns)

Find all the superfluous attributes in R, the core of R and the reducts of R Choose one of the reducts and limit the subsequent steps to this reduct.

Step 2: SIMPLIFYING OF SUBSEQUENT RULES

(Deletion of some row entries)

Find the core of each rule ri (set of necessary attributes). For each rule ri find the set of its reducts RED(ri)={ri1, ri2… }.

Step 3: SIMPLIFYING FINAL (DISJUNCTIVE) RULES

(Merging rows, and then deletion of certain merged row components)

For each combination of decision attribute values create one final disjunctive rule. Find the reducts of all the disjunctive rules.

EXAMPLE – Initial knowledge

a b c d e

x1 1 0 0 1 1

x2 1 0 0 0 1

x3 0 0 0 0 0

x4 1 1 0 1 0

x5 1 1 0 2 2

x6 2 2 0 2 2

x7 2 2 2 2 2

Initial decision table T Corresponding set of rules R

r1: a1b0c1d1→e1

r2: a1b0c0d0→e1

r3: a0b0c0d0→e0

r4: a1b1c0d1→e0

r5: a1b1c0d2→e2

r6: a2b2c0d2→e2

r7: a2b2c2d2→e2

Our goal: maximally reduce number of rules and number of components in the predecessors.

STEP 1 – Simplification of the Set of Rules

Explanation. Attribute c is superfluous (the column c can be deleted), because all the decision rules without the attribute c are true (after deletion of c-formulas from rules there will be no inconsistent rules in new rule set).

Superfluous attributes: cNecessary attributes: a, b, dCORE(R)={a,b,d}RED(R)={a,b,d}

New decision table T’

a b d e

x1 1 0 1 1

x2 1 0 0 1

x3 0 0 0 0

x4 1 1 1 0

x5 1 1 2 2

x6 2 2 2 2

x7 2 2 2 2

STEP 2 – Simplification of Rules Table with superfluous attributes, cores and reducts of subsequent rules

Table of rule’s reducts rij (rij means j-th reduct of ri; cores are red)

Rules Superfluous attr. Cores Reducts

r1 a, d {b} {b,a}, {b,d}

r2 b, d {a} {a,b}, {a,d}

r3 b, d {a} {a}

r4 a {b,d} {b,d}

r5 a, b {d} {d}

r6 a, b, d none {a}, {b}, {d}

Reducts of ri a b d e

r11 1 0 x 1

r12 x 0 1 1

r21 1 0 x 1

r22 1 x 0 1

r31 0 x x 0

Reducts of ri a b d e

r41 x 1 1 0

r51 x x 2 2

r61 2 x x 2

r62 x 2 x 2

r63 x x 2 2

STEP 3 – Simplification of Final Rules Each final rule has the form of zi: piqi, where qi is one of the successors of intermediate rules rij (i.e. e0, e1 or e2) and pi is disjunction of all predecessors of rules rij with succesor qi.

To simplify the final rule, i.e. to find its reduct, we need to delete from its predecessor all the superfluous components of the disjunction pi. During this procedure we have to specify the meanings of different formulas f, i.e. sets | f |.

Below we list subsequent final rules zi and reducts of this rules.

Final rule z1: p1q1, that is (a1b0)(b0d1)(a1d0)e1

Successor of rule: q1= e1, | q1 |={x1,x2}Predecessor of rule: p1=(a1b0)(b0d1)(a1d0), | p1 |={x1,x2} p11=(a1b0), | p11 |={x1,x2} p12=(b0d1), | p12 |={x2} p13=(a1d0), | p13 |={x2}Superfluous components: {p12,p13}Necessary components: {p11}Reduct of rule: p11q1, that is a1b0e1

STEP 3 – ContinuationFinal rule z2: p2q2 , that is a0(b1d1)e0

Successor of rule: q2= e0, | q2 |={x3,x4}Predecessor of rule: p2= a0(b1d1), | p2 |={x3,x4} p21=a0, | p21|={x3} p22=(b1d1), | p22 |={x4}Superfluous components: noneNecessary components: {p21,p22}Reduct of rule: p21p22q2, that is a0(b1d1)e0 (reduction didn’t occure)

Final rule z3: p3q3, that is a2b2d2e2

Successor of rule: q3= e2, | q3 |={x5,x6,x7}Predecessor of rule: p3= a2b2d2, | p3 |={x5,x6,x7} p31=a2, | p31 |={x6,x7} p32=b2, | p32 |={x6,x7} p33=d2, | p33 |={ x5,x6,x7}Superfluous components: {p31,p32}Necessary components: {p33}

Reduct of rule: p33q3, that is d2e2

RESULT – Simplified Set od Rules

Finally we obtain three rules instead of seven. Each rule contains, besides second rule that is disjunctive, less atomic formulas than original rules.

a1b0e1

a0(b1d1)e0

d2e2

New rules:

STUDY CASE

Why Polish Adjective Declension ?

Answer: Polish Adjective Declension is an application domain with a well-defined borderline; i.e.: in which the total function generates all the combinatory possibilities.

Case = {Nominative, Accusative, Genitive, Dative, Instrumental, Locative}

Number = {singular, plural}

Gender = {masculine, feminine, neuter, X, Y, Z*}

POLISH DECLENSION

In Polish School Grammar, the Adjective declension consists in amalgamation of 3 “morphological categories”.In our experimentation, we interpreted these categories as attributes of an information system. (Rough Set Theory, Pawlak Z., 1982)

* X, Y, Z will be analyzed in the sequel.

THE PROBLEM OF GENDER IN POLISH

• In Slavic languages, Gender is a classificatory category as for Nouns while it is an inflectional category as for Adjectives.

• In order elucidate the problem of Gender in Polish noun morphology, we built a database of usages (not uses) of the proximal deictic adjectives.

• The root of these adjectives is very short: one single phoneme t-.

THE DEICTIC MORPHEMES IN POLISH

The Nominative form of Polish morphemes with proximal (with respect to the speaker) deictic meaning are:

TEN, TA, TO

They correspond to :

TEN TA TO

English this this this

French ce cette ce

German dieser diese dieses

Japanese kono kono kono

SAMPLES FROM OUR DATABASE

Some samples from the db (examples only in the Nominative case)

Polish English translationSingular Plural

Feminineta deska te deski this/these board(s)ta gęś te gęsi this/these goose/geeseta pani te panie this/these lady/ladies

Masculineten dom te domy this/these house(s)ten pies te psy this/these dog(s)ten pan ci panowie this/these sir(s)

Neuterto pióro te pióra this/these feather(s)to kurczę te kurczęta this/these chicken(s)to dziecko te dzieci this/these child/children... ... ...

Our database contains 108 different noun phrases totally combining all the categories involved in the declension: Case, Number, Gender and Animacy)

Defining Gender in Polish7 “Genders”

In Polish Linguistics (cf. SALONI, Z. 1976), Gender is defined as a morpho-syntactic category. It is in the Accusative Case that Gender forms of Polish Adjectives are mostly differentiated. Sub-genders are distinguished in singular and in plural. Doing so, surprisingly, up to 7 gender classes have been proposed :

* “Animal” corresponds to the feature “animate” in other European languages descriptions.** “Personal” corresponds to the feature “human” .*** Pluralia tantum are defective nouns with no singular form).

Singular :1. feminine (with a specific Accusative form)2. neuter (with the same form in Accusative as in Nominative)3. animal* masculine (with the same form in Accusative as in Genitive)4. non animal masculine (with the same form in Accusative as in Nominative)Plural :1. personal** masculine (with the same form in Accusative as in Genitive),2. non personal masculine (with the same form in Accusative as in Nominative)3. “pluralia tantum”*** (with the same form in Accusative as in Nominative)

Defining Gender in Polish5 “Genders”

In fact, Saloni’s theory derives from that of Mańczak, W. (1956) who distinguished the following five “sub-genders” only :

1. personal masculine2. animal masculine3. non animal masculine4. feminine5. neuter

DATABASE WITH 7 GENDERSNb of objects : 108Nb of duplicates : 65

Nb of attributes : 3 (with respectively 2, 7, 6 values)Nb->{plur or sing}Gnd->{fem or mascAn or mascHum or mascInan or neu or nMasHum or plTant}Case->{A or D or G or I or L or N}Theoretical Combinations : 84Apparent Saturation Index : 51.19%

Non Attested Pairs of Values (10)If all non-attested pairs are inconsistent,the maximum number of combinations is : 54Corrected Saturation Index : 79.63%

Our knowledge reduction algorithm Our knowledge reduction algorithm cannotcannot reduce the different reduce the different descriptions. Instead 45 decision rules are proposed.descriptions. Instead 45 decision rules are proposed.Our knowledge reduction algorithm Our knowledge reduction algorithm cannotcannot reduce the different reduce the different descriptions. Instead 45 decision rules are proposed.descriptions. Instead 45 decision rules are proposed.

CRITICAL REMARKS ON SUB-GENDERS

We observed that the 5, 6, 8 or 9 “sub-genders” of Polish School Grammars (a) neither correspond to any known semantic or ontological categories (b) nor to any known grammatical sub-gender in other languages.

In inflectional languages, morphological amalgamation of several different categories in one single form may be the source of difficulties in discerning properly the semantic categories in question.

ANALYSIS

of

GENDER SUBCATEGORIZATION

in POLISH GRAMMAR

DB building

Using our “Dynamic db Builder”… morpheme

sample

attribute, value(features chosen for each entry)

Multi-valued Contingency Table

The 108 samples are collected into a Multi-valued Contingency Table

FIRST TRIAL

SPLITTING GENDER

Observing the singular/plural oppositions in Adjective declension, we first divided the 7 “sub-genders” valued Gender attribute into 3 attributes :

gender = {feminine, neuter, masculine)animacy = {animate, inanimate}humanity = {human, non human}

We split the 7 “sub-genders”-valued Gender attribute into more than one attribute (with less values each).

FIRST TRIAL - RESULTS SPLITTING GENDER

Objects : 108Duplicates : 0Duplicate ratio : 0%The following pairs of attributes could be merged:[HUM|INA] Confidence index = 99.9%[HUM|nHUM]Confidence index = 99.9%[INA|nHUM]Confidence index = 99.9%Attributes : 5 (with resp. 6,2,3,2,2 values)case, number, gender, animacy and humanityTheoretical Combinations : 144Apparent Saturation Index : 75%Non-Attested Pairs of Values (1)If all non-attested pairs were inconsistent,the maximum number of combinations would be: 108Corrected Saturation Index : 100%======================================================Non Attested Pairs of Values (1)inanimate, human, 2, 4

Our knowledge reduction algorithm reduces the 108 different Our knowledge reduction algorithm reduces the 108 different descriptions to 34 decision rules.descriptions to 34 decision rules.Our knowledge reduction algorithm reduces the 108 different Our knowledge reduction algorithm reduces the 108 different descriptions to 34 decision rules.descriptions to 34 decision rules.

SECOND TRIAL MERGING ANIMACY with HUMANITYConsidering the results of the first trial

- one pair of values (inanimate and human) being not attested in the db (in fact, this pair is clearly contradictory)Non Attested Pairs of Values (1)inanimate, human, 2, 4

- and the confidence indices being computed as belowThe following pairs of attributes could be merged:[HUM|INA] Confidence index = 99.9%[HUM|nHUM] Confidence index = 99.9%[INA|nHUM] Confidence index = 99.9%

we decided to merge both binary attributes ANIMACY with HUMANITY into one three-valued attribute as follows :

ANIMACY-*-{ANY}=[nhuman|inanimate|human]

SECOND TRIAL - RESULTS

MERGING ANIMACY with HUMANITYNb of objects : 108Nb of duplicates : 0Nb of attributes : 4 (with respectively 2, 3, 3 and 6 values)Nb-->{plur or sing}Gnd-->{fem or masc or neu }Anim--> {inanim or anim or animHum}Case-->{A or D or G or I or L or N}

Duplicate ratio : 0%Theoretical Combinations : 108Apparent Saturation Index : 100%Non-Attested Pairs of Values (0)Corrected Saturation Index : 100%

Again our knowledge reduction algorithm reduces the 108 different Again our knowledge reduction algorithm reduces the 108 different descriptions to 34 decision rules.descriptions to 34 decision rules.Again our knowledge reduction algorithm reduces the 108 different Again our knowledge reduction algorithm reduces the 108 different descriptions to 34 decision rules.descriptions to 34 decision rules.

Establishingan ANIMACY CATEGORY

for Polish Grammar

KNOWLEDGE REDUCTIONusing SEMANA

The knowledge reduction algorithm The knowledge reduction algorithm reduces the 108 different descriptions of reduces the 108 different descriptions of Polish Proximal Deictic Morphemes to Polish Proximal Deictic Morphemes to 34 decision rules.34 decision rules.

The knowledge reduction algorithm The knowledge reduction algorithm reduces the 108 different descriptions of reduces the 108 different descriptions of Polish Proximal Deictic Morphemes to Polish Proximal Deictic Morphemes to 34 decision rules.34 decision rules.

34 Morphological Rulesr1 (9) : CASdat,NBRplu --> tymr2 (3) : CASins,GNDmas,NBRsin --> tymr3 (3) : CASins,GNDneu,NBRsin --> tymr4 (3) : CASloc,GNDmas,NBRsin --> tymr5 (3) : CASloc,GNDneu,NBRsin --> tym

r6 (9) : CASins,NBRplu --> tymi

r7 (1) : CASacc,ANYhum,GNDmas,NBRplu --> tychr8 (9) : CASgen,NBRplu --> tychr9 (9) : CASloc,NBRplu --> tych

r10 (3) : CASacc,GNDneu,NBRsin --> tor11 (3) : CASnom,GNDneu,NBRsin --> to

r12 (3) : CASacc,ANYina,NBRplu --> ter13 (3) : CASacc,ANYnhu,NBRplu --> ter14 (3) : CASacc,GNDfem,NBRplu --> ter15 (3) : CASacc,GNDneu,NBRplu --> ter16 (3) : CASnom,ANYina,NBRplu --> ter17 (3) : CASnom,ANYnhu,NBRplu --> ter18 (3) : CASnom,GNDfem,NBRplu --> ter19 (3) : CASnom,GNDneu,NBRplu --> te

r20 (1) : CASacc,ANYina,GNDmas,NBRsin --> tenr21 (3) : CASnom,GNDmas,NBRsin --> ten

r22 (3) : CASdat,GNDmas,NBRsin --> temur23 (3) : CASdat,GNDneu,NBRsin --> temu

r24 (3) : CASdat,GNDfem,NBRsin --> tejr25 (3) : CASgen,GNDfem,NBRsin --> tejr26 (3) : CASloc,GNDfem,NBRsin --> tej

r27 (1) : CASacc,ANYhum,GNDmas,NBRsin --> tegor28 (1) : CASacc,ANYnhu,GNDmas,NBRsin --> tegor29 (3) : CASgen,GNDmas,NBRsin --> tegor30 (3) : CASgen,GNDneu,NBRsin --> tego

r31 (3) : CASacc,GNDfem,NBRsin --> te*

r32 (3) : CASnom,GNDfem,NBRsin --> ta

r33 (3) : CASins,GNDfem,NBRsin --> ta*

r34 (1) : CASnom,ANYhum,GNDmas,NBRplu --> ci

DISCOVERED KNOWLEDGE1. All the 108 different descriptions can be represented by 34 rules only.2. 20 rules represent the singular forms and 14 rules represent the plural forms.3. The Gender attribute is not necessary in 8 rules in plural and in cases other than

Nominative. This confirms the generally observed fact that, in Polish grammar, in the plural oblique cases, gender is neutralized (no Gender distinction).

4. The Attribute “Animacy” is present in 9/34 rules and 17/108 samples.3 rules contain the value Human (hum)

r07 (1) : CASacc,ANYhum,GNDmas,NBRplu --> tychr27 (1) : CASacc,ANYhum,GNDmas,NBRsin --> tegor34 (1) : CASnom,ANYhum,GNDmas,NBRplu --> ci

3 rules contain the value Inanimate (ina)r20 (1) : CASacc,ANYina,GNDmas,NBRsin --> tenr12 (3) : CASacc,ANYina,NBRplu --> ter16 (3) : CASnom,ANYina,NBRplu --> te

3 rules contain the value non Human (nhu)r17 (3) : CASnom,ANYnhu,NBRplu --> ter13 (3) : CASacc,ANYnhu,NBRplu --> ter28 (1) : CASacc,ANYnhu,GNDmas,NBRsin --> tego

GENDER and ANIMACY

The 7 genders theory proposed a too coarse-grained analysis of the domain using only one attribute supposed to represent the Gender category.

In our “first trial”, in addition to Gender, two binary categories (Human and Animate ) were introduced resulting, as a matter of fact, in a too fine-grained description of the domain.

In our “second trial”, after having merged the two binary categories, we got one three-valued Animacy category. As a result, the Analyser (1) detects none of the following anomalies: duplicates (of usages, not uses), non attested pairs of values and (2) proposed no attribute merging possibilities.

Needless to say that our theory takes into account the definition of Gender category such as it is generally used in grammars of other languages.

The ONTOLOGICAL STRUCTUREof ANIMACY

Interestingly, we noticed that the Feature Structure of Animacy Attribute being a binary tree, it is normal that its values are all exclusive by the law of the excluded middle: nothing can be true and false at the same time.

ANIMACY

HUMANITY

non animate non human human

- +

- +

RELATIVE WEIGHTOF THE ANIMACY ATTRIBUTE

If we consider the relative weight of the ANIMACY attribute (only 5.4%), we can better understand the difficulties that Polish linguists encountered in their work.

Relative weight of attributes N weight(%)1.CAS 116 36.62.NBR 116 36.63.GND 68 21.54.ANY 17 5.4

It becomes clear that ANIMACY is not as important a category as the other three ones (Case, Number and Gender) which co-occur in the amalgamated adjective paradigm.

BURT TABLE acc dat gen ins loc nom hum ina nhu fem mas neu plu sin ci ta ta* te te* tego tej tem ten to tych tym tymi acc 18 0 0 0 0 0 6 6 6 6 6 6 9 9 0 0 0 8 3 2 0 0 1 3 1 0 0 dat 0 18 0 0 0 0 6 6 6 6 6 6 9 9 0 0 0 0 0 0 3 6 0 0 0 9 0 gen 0 0 18 0 0 0 6 6 6 6 6 6 9 9 0 0 0 0 0 6 3 0 0 0 9 0 0 ins 0 0 0 18 0 0 6 6 6 6 6 6 9 9 0 0 3 0 0 0 0 0 0 0 0 6 9 loc 0 0 0 0 18 0 6 6 6 6 6 6 9 9 0 0 0 0 0 0 3 0 0 0 9 6 0 nom 0 0 0 0 0 18 6 6 6 6 6 6 9 9 1 3 0 8 0 0 0 0 3 3 0 0 0 hum 6 6 6 6 6 6 36 0 0 12 12 12 18 18 1 1 1 4 1 3 3 2 1 2 7 0 0 ina 6 6 6 6 6 6 0 36 0 12 12 12 18 18 0 1 1 6 1 2 3 2 2 2 6 7 3 nhu 6 6 6 6 6 6 0 0 36 12 12 12 18 18 0 1 1 6 1 3 3 2 1 2 6 7 3 fem 6 6 6 6 6 6 12 12 12 36 0 0 18 18 0 3 3 6 3 0 9 0 0 0 6 3 3 mas 6 6 6 6 6 6 12 12 12 0 36 0 18 18 1 0 0 4 0 5 0 3 4 0 7 9 3 neu 6 6 6 6 6 6 12 12 12 0 0 36 18 18 0 0 0 6 0 3 0 3 0 6 6 9 3 plu 9 9 9 9 9 9 18 18 18 18 18 18 54 0 1 0 0 16 0 0 0 0 0 0 19 9 9 sin 9 9 9 9 9 9 18 18 18 18 18 18 0 54 0 3 3 0 3 8 9 6 4 6 0 12 0 ci 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ta 0 0 0 0 0 3 1 1 1 3 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 ta* 0 0 0 3 0 0 1 1 1 3 0 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 te 8 0 0 0 0 8 4 6 6 6 4 6 16 0 0 0 0 16 0 0 0 0 0 0 0 0 0 te* 3 0 0 0 0 0 1 1 1 3 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 tego 2 0 6 0 0 0 3 2 3 0 5 3 0 8 0 0 0 0 0 8 0 0 0 0 0 0 0 tej 0 3 3 0 3 0 3 3 3 9 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 tem 0 6 0 0 0 0 2 2 2 0 3 3 0 6 0 0 0 0 0 0 0 6 0 0 0 0 0 ten 1 0 0 0 0 3 1 2 1 0 4 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 to 3 0 0 0 0 3 2 2 2 0 0 6 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 tych 1 0 9 0 9 0 7 6 6 6 7 6 19 0 0 0 0 0 0 0 0 0 0 0 19 0 0 tym 0 9 0 6 6 0 7 7 7 3 9 9 9 12 0 0 0 0 0 0 0 0 0 0 0 21 0 tymi 0 0 0 9 0 0 3 3 3 3 3 3 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 FJ 90 90 90 90 90 90 180 180 180 180 180 180 270 270 5 15 15 80 15 40 45 30 20 30 95 105 45

BURT TABLE acc dat gen ins loc nom hum ina nhu fem mas neu plu sin ci ta ta* te te* tego tej tem ten to tych tym tymi acc 18 0 0 0 0 0 6 6 6 6 6 6 9 9 0 0 0 8 3 2 0 0 1 3 1 0 0 dat 0 18 0 0 0 0 6 6 6 6 6 6 9 9 0 0 0 0 0 0 3 6 0 0 0 9 0 gen 0 0 18 0 0 0 6 6 6 6 6 6 9 9 0 0 0 0 0 6 3 0 0 0 9 0 0 ins 0 0 0 18 0 0 6 6 6 6 6 6 9 9 0 0 3 0 0 0 0 0 0 0 0 6 9 loc 0 0 0 0 18 0 6 6 6 6 6 6 9 9 0 0 0 0 0 0 3 0 0 0 9 6 0 nom 0 0 0 0 0 18 6 6 6 6 6 6 9 9 1 3 0 8 0 0 0 0 3 3 0 0 0 hum 6 6 6 6 6 6 36 0 0 12 12 12 18 18 1 1 1 4 1 3 3 2 1 2 7 0 0 ina 6 6 6 6 6 6 0 36 0 12 12 12 18 18 0 1 1 6 1 2 3 2 2 2 6 7 3 nhu 6 6 6 6 6 6 0 0 36 12 12 12 18 18 0 1 1 6 1 3 3 2 1 2 6 7 3 fem 6 6 6 6 6 6 12 12 12 36 0 0 18 18 0 3 3 6 3 0 9 0 0 0 6 3 3 mas 6 6 6 6 6 6 12 12 12 0 36 0 18 18 1 0 0 4 0 5 0 3 4 0 7 9 3 neu 6 6 6 6 6 6 12 12 12 0 0 36 18 18 0 0 0 6 0 3 0 3 0 6 6 9 3 plu 9 9 9 9 9 9 18 18 18 18 18 18 54 0 1 0 0 16 0 0 0 0 0 0 19 9 9 sin 9 9 9 9 9 9 18 18 18 18 18 18 0 54 0 3 3 0 3 8 9 6 4 6 0 12 0 ci 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ta 0 0 0 0 0 3 1 1 1 3 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 ta* 0 0 0 3 0 0 1 1 1 3 0 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 te 8 0 0 0 0 8 4 6 6 6 4 6 16 0 0 0 0 16 0 0 0 0 0 0 0 0 0 te* 3 0 0 0 0 0 1 1 1 3 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 tego 2 0 6 0 0 0 3 2 3 0 5 3 0 8 0 0 0 0 0 8 0 0 0 0 0 0 0 tej 0 3 3 0 3 0 3 3 3 9 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 tem 0 6 0 0 0 0 2 2 2 0 3 3 0 6 0 0 0 0 0 0 0 6 0 0 0 0 0 ten 1 0 0 0 0 3 1 2 1 0 4 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 to 3 0 0 0 0 3 2 2 2 0 0 6 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 tych 1 0 9 0 9 0 7 6 6 6 7 6 19 0 0 0 0 0 0 0 0 0 0 0 19 0 0 tym 0 9 0 6 6 0 7 7 7 3 9 9 9 12 0 0 0 0 0 0 0 0 0 0 0 21 0 tymi 0 0 0 9 0 0 3 3 3 3 3 3 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 FJ 90 90 90 90 90 90 180 180 180 180 180 180 270 270 5 15 15 80 15 40 45 30 20 30 95 105 45

Correspondence Factor Analysis (CFA)Correspondence Factor Analysis (CFA)

Numbers in the Table are considered as coordinates of points in a N-dimensional space.

•• •••••• •

•••••• •••

•••••• ••••••

••• •••

•••••• •••• •••••• •

••••••

••••

z

x

y

F1

F2

F3

CFA calculates the axes of inertia of the cloud of points (F1, F2, F3 …)

and displaysprojections in planes [F1,F2], [F1,F3], etc.

CFA is implemented as “Stat-3” in “Semana”

Proj. In plane [1,2] PROJECTION DANS LE PLAN FACTORIEL [1,2]| Horizontal: Axe #2 (Inertie: 12.81%) ——— Vertical: Axe #1 (Inertie: 13.05%)| Largeur: 1.798197; Hauteur: 2.123853; Nombre de points : 27+--------------------------------------------------+--------------------tem------------+--10| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | tej | 00| | | 00| | | 00| | dat | 00| | | 00| sin| | 00| te* tego | | 10ta to ten | | 00| | | 00| | | 00| | | 00| | | 00| | tym ta* | 00| | | 00| | | 00| | | 00| | | 00+-----------------------------------------------inahum---gen---------------------------+--40| nhumas | 20| nom acc fem| | 10| neu| loc | 00| | | 00| | | 00| | | 00| | | 00| | ins | 00| | | 00| | | 00| | | 00| plu | 00| | | 00| ci | tych | 10| te | | 00| | | 00| | | 00| | | 00| | | 00| | tymi| 00+--------------------------------------------------+-----------------------------------+--00

axis 2

axis 1

3 6 43

1619

9

21

9

8

6

3

Qualifiers = animacy, gender

Quantifiers = number

Syntactic relators = cases

morphemes

Qualifiers = animacy, gender

Quantifiers = number

Syntactic relators = cases

morphemes

Projection in plane [1,2]

PROJECTION DANS LE PLAN FACTORIEL [1,2]| Horizontal: Axe #2 (Inertie: 12.81%) ——— Vertical: Axe #1 (Inertie: 13.05%)| Largeur: 1.798197; Hauteur: 2.123853; Nombre de points : 27+--------------------------------------------------+--------------------------------temu+--10| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| tej | | 00| | | 00| | | 00| | dat | 00| | | 00| sin | | 00| te* tego | 00| ta | to ten | 00| | | 00| | | 00| | | 00| | | 00ta* | tym | 00| | | 00| | | 00| | | 00| | | 00+--------------------------------------gen------inahum--------------------------------+--40| nhu| mas | 20| fem acc| nom | 10| loc | neu | 00| | | 00| | | 00| | | 00| | | 00| ins| | 00| | | 00| | | 00| | | 00| |plu | 00| | | 00| tych ci | 10| | te | 00| | | 00| | | 00| | | 00| | | 00| tymi | | 00+--------------------------------------------------+-----------------------------------+--00

axis 4

axis 1

• morphemes ta*, te*, tej, ta are only associated to feminine

• morphemes tego, to, ten, temu, ci are only associated to masculine or neutral

• morphemes ta*, te*, tej, ta are only associated to feminine

• morphemes tego, to, ten, temu, ci are only associated to masculine or neutral

Again, tym is ambiguous and may

be associated to any gender

Again, tym is ambiguous and may

be associated to any gender

Axis 4 separates gender:Axis 4 separates gender:feminine vsvs {masculine, neutral}

Note that animacy is still not

differenciated on axis 4.

Differenciation appears only on axis 9 !

Note that animacy is still not

differenciated on axis 4.

Differenciation appears only on axis 9 !

Differenciation of Animacy does not appear before factor 9Differenciation of Animacy does not appear before factor 9 FREQ QLT INR | F#1 COR CTR | F#2 COR CTR | F#3 COR CTR | F#4 COR CTR |—————————————————————————————————————————————————————————————————————————————————hum 67 5 23 | 0 0 0 | 29 2 0 | -34 3 1 | -5 0 0 |ina 67 5 23 | -1 0 0 | -26 2 0 | 34 3 1 | -6 0 0 |nhu 67 0 22 | 1 0 0 | -3 0 0 | 0 0 0 | 11 0 0 |acc 33 397 40 | -70 3 1 | -745 391 120 | 47 2 1 | 48 2 1 |dat 33 588 42 | 643 272 88 | 483 153 50 | 97 6 2 | -489 157 66 |gen 33 596 40 | -15 0 0 | 153 16 5 | -870 522 186 | 290 58 23 |ins 33 869 48 | -362 77 28 | 682 271 100 | 924 499 210 | 195 22 11 |loc 33 326 35 | -117 11 3 | 366 106 29 | -504 201 62 | 103 8 3 |nom 33 633 44 | -78 4 1 | -938 556 190 | 306 59 23 | -147 14 6fem 67 768 33 | 20 1 0 | -26 1 0 | 85 12 4 | 669 754 247 |mas 67 245 28 | -9 0 0 | 56 6 1 | -97 19 5 | -332 220 61neu 67 232 28 | -11 0 0 | -29 2 0 | 12 0 0 | -336 229 63 |plu 100 873 30 | -546 823 189 | 44 5 1 | -68 13 3 | -108 32 10 |sin 100 873 30 | 546 823 189 | -44 5 1 | 68 13 3 | 108 32 10 |ci 2 76 36 | -644 18 5 | -840 30 8 | 128 1 0 | -804 28 10 |ta 6 276 40 | 497 29 9 |-1046 127 39 | 545 35 12 | 856 85 34 |ta* 6 445 40 | 207 5 2 | 635 47 15 | 1278 190 67 | 1321 203 80 |te 30 651 44 | -630 225 75 | -839 399 135 | 148 12 5 | -156 14 6 |te* 6 265 40 | 505 30 9 | -845 83 26 | 237 7 2 | 1121 146 58 |tego 15 249 42 | 516 79 25 | -92 2 1 | -751 167 62 | 6 0 0 |tej 17 588 42 | 749 187 60 | 274 25 8 | -324 35 13 | 1012 341 142 |temu 11 559 44 | 1200 306 102 | 469 47 16 | 145 4 2 | -973 201 87 |ten 7 208 39 | 469 34 10 | -918 132 40 | 262 11 4 | -441 30 12 |to 11 308 41 | 468 50 15 | -948 204 65 | 305 21 8 | -378 32 13 |tych 35 812 44 | -623 263 87 | 264 47 16 | -858 498 191 | 86 5 2 |tym 39 481 35 | 215 43 11 | 527 256 70 | 174 28 9 | -408 154 54 |tymi 17 726 47 | -924 251 91 | 753 167 61 | 1016 304 127 | 119 4 2 |

| F#5 COR CTR | F#6 COR CTR | F#7 COR CTR | F#8 COR CTR | F#9 COR CTR |————————————————————————————————————————————————————————————————————————————————————hum | 27 2 0 | -68 11 3 | 19 1 0 | -19 1 0 | 503 617 322 |ina | -34 3 1 | -0 0 0 | -25 2 1 | 87 19 8 | -309 235 121 |nhu | 7 0 0 | 68 11 3 | 6 0 0 | -69 12 5 | -194 94 48 |acc | 160 18 9 | 721 366 191 | -386 105 68 | 209 31 23 | 85 5 5 |dat | -603 239 121 | 126 10 6 | -246 40 27 | -321 68 55 | 10 0 0 |gen | 526 191 92 | -102 7 4 | 13 0 0 | -431 128 99 | -72 4 3 |ins | 446 116 66 | -40 1 1 | 45 1 1 | 24 0 0 | -5 0 0 |loc | -357 101 42 | -72 4 2 | 318 80 46 | 649 333 224 | 8 0 0 |nom | -172 19 10 | -633 253 147 | 255 41 30 | -129 11 9 | -26 0 0 |fem | -317 170 67 | 0 0 0 | -74 9 5 | -94 15 9 | 12 0 0 |mas | 214 92 31 | -311 193 71 | -374 280 128 | 179 64 34 | -13 0 0 |neu | 103 22 7 | 310 195 71 | 448 407 183 | -85 15 8 | 1 0 0 |plu | -163 73 26 | 31 3 1 | -64 11 6 | -90 22 13 | 2 0 0 |sin | 163 73 26 | -31 3 1 | 64 11 6 | 90 22 13 | -2 0 0 |ci | -161 1 0 |-1931 159 76 | -466 9 6 | -233 2 2 | 3212 441 364 |ta | -563 37 18 |-1309 199 105 | 699 57 37 | -528 32 25 | -110 1 1 |ta* | 501 29 14 | -141 2 1 | 100 1 1 | 77 1 1 | 38 0 0 |te | -342 66 35 | 242 33 19 | -242 33 24 | -278 44 37 | -209 25 25 |te* | 10 0 0 | 1359 215 113 |-1121 146 95 | 809 76 58 | 654 50 45 |tego | 1333 526 263 | -11 0 0 | -241 17 12 | -445 59 47 | -24 0 0 |tej | -516 89 44 | -93 3 2 | 55 1 1 | -152 8 6 | -53 1 1 |temu | -485 50 26 | 187 7 4 | -409 36 25 | -728 113 94 | 14 0 0 |ten | 481 36 17 |-1255 247 128 | -627 62 40 | 975 149 112 | -622 61 55 |to | 448 46 22 | 637 92 50 | 1269 366 245 | 177 7 6 | 197 9 8 |tych | -106 8 4 | -65 3 2 | 152 16 11 | 129 11 9 | 13 0 0 |tym | -205 39 16 | 35 1 1 | 81 6 4 | 374 129 87 | 11 0 0 |tymi | 488 70 40 | -17 0 0 | -56 1 1 | -263 20 18 | -21 0 0 |

Animacy first

appears on factor 9

PROJECTION DANS LE PLAN FACTORIEL [1,9]| Horizontal: Axe #1 (Inertie: 13.05%) ——— Vertical: Axe #9 (Inertie: %)| Largeur: 2.123853; Hauteur: 3.83365; Nombre de points : 27+--------ci ---------------------------+-----------------------------------------------+--10| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | | 00| | te* | 00| | | 00| hum| | 00| | | 00| | | 00| | to | 00| | | 00| acc | ta* | 00+-----------tycplu---ins---------locfem+-----tym---------tegsindat------------------tem+--40tymi nomgen| ta tej | 02| te nhu| | 00| | | 00| ina| | 00| | | 00| | | 00| | ten | 00+--------------------------------------+-----------------------------------------------+--00

axis 1

axis 9(inertia = 4.35 %)

Axis 9 separates Axis 9 separates human vsvs {nonHuman, inanimate}

morpheme ci applies only to human entitiesmorpheme ci applies only to human entities

Masculine is “unmarked” in Polish utterances

Matka i dziecko nie mogli się sobą nacieszyć.(The mother and her child were gazing at each other.)

Obviously, none of the statements below can be true:- *GENDER is a subcategory of ANIMACY - *ANIMACY is a subcategory of GENDER On the contrary, it is easy to admit that:HUMAN is a subcategory of ANIMACY.

We claim that Attributes with “heterogeneous” values do not exist.Consequently, the presumed “syncretism” of GENDER and ANIMACY is meaningless.

NOUN, fem, hum“mother”

NOUN, neu, hum“child”

VERB, mas, hum“can”

Comparing Theories of Polish Gender

THEORIES GRAMMATICALIZED ATTRIBUTES

1956 - Mańczak W. (5)1976 - Saloni Z. (7)2001 - Woliński M. (8)2003 Przepiórkowski A. (9)

GENDER

feminineneuter

non animal masculineanimal masculine

personal masculinenon personal masculine

“pluralia tantum”

This proposal (3 values of GENDER)(3 values of ANIMACY)

GENDER ANIMACY

feminine

neuter

masculine

inanimate

non human animate

human animate