Defending that Grammaticality can be explained through a Fuzzy - PowerPoint PPT Presentation

LACOMPLING 2018 Symposium on Logic and Algorithms in Computational Linguistics 2018 Stockholm, 28 –31 August 2018 A DRIÀ T ORRENS U RRUTIA D EPARTAMENT DE F ILOLOGIES R OMÀNIQUES U NIVERSITAT R OVIRA I V IRGILI T ARRAGONA

Defending that Grammaticality can be explained through a Fuzzy Grammar Grammaticality as an Uncertain/Fuzzy value Tools for taking into account Grammaticality Fuzzy Grammar as a model to explain Grammaticality in terms of Degrees

Discrete Theoretical Approach • PERFECT • Degrees here are not Competence a deal either don’t exist • IMPERFECT • IMPERFECT Performance • Degrees of Acceptability • ( Psycholinguistic ) “ To give up the notion that a grammar defines a set of well-formed utterances is to give up a great deal […] If we can maintain the concept of discrete grammaticality, we will be in a better position to pursue an understanding of grammatical universals ” Bever (1975:601). Sobre la idealización del lenguaje “The only reasonable way to approach a grasp of reality” Chomsky (1998:115).

Natural Natural Language Language Processing Processing Do Do we we evaluate evaluate non non- -grammatical grammatical inputs? inputs? PERFECT input ------------- -—-------- + Deep +Closer to thinking - Deep +Closer performance

Natural Natural Language Language Processing Processing We We Do Do Evaluate Evaluate Inputs Inputs This guy doesn’t speak very well --X----X--- input X---X---- X—X-------- X OBJECTIVE: OUR MACHINES HAVE TO BOTH UNDERSTAND/PARSE AND EVALUATE THE NATURAL LANGUAGE INPUTS, AS HUMANS DO ------X--- input X-------X— X--------X INPUT: GRAMMATICALITY AT 85% SELF-TAUGHT LANGUAGE LEARNING SOFTWARES

Linguistic modules Phonetics Pragmatics Morphology LINGUISTIC COMPETENCE Prosody Syntax Semantics

THIS WORK IS ASSEMBLED ON GRAMMATICALITY Spanish Syntax

FUZZY GRAMMAR FUZZY LOGIC GRAMMARS WITH GRADIENT EVALUATIVE SYSTEMS CONSTRAINTS

DISCRETE VS FUZZY CLASSICAL LOGIC <1,0> FUZZY LOGIC: [1,0]

DESCRIBING EVERY KIND OF LINGUISTIC INPUT (FUZZY) DISCRETE GRAMMAR: AN INPUT IS EITHER LINGUISTIC GRAMMATICAL O NON- INPUT GRAMMATICAL LINGUISTIC LINGUISTIC INPUT INPUT FUZZY GRAMMAR: AN INPUT IS % GRAMMATICAL

FUZZY REASONING IF-THEN RULES IF THE VALUE OF GRAMMATICALITY IS HIGH, THEN THE VALUE OF NON-GRAMMATICALITY IS LOW

TYPE THEORY HIGH ORDER FUZZY LOGIC The basic concept in FTT is type (denoted by Greek letters) Atomic types are  representing elements Type o (omicron) is the type of truth degree FTT Vilem Novak, (2005) In the semantics In the semantics the type  is assigned a set  M  whose elements can be anything   [0,1] In the semantics it is a  [0,1] A set of truth values M o Representing various degrees, Which in our case is M o = [0,1] Grammaticality, Complexity, etc.

Defining a Fuzzy Set B : M  [0,1] Membership Function Set Degree (Universe) (ROL in U) Linguistic Knowledge of a Group: Linguistic Knowledge of a Group:  M o [0,1] CL: M  x M   M o  Complex types, set of functions M  o

Example of a Module in a Fuzzy Grammar X: X  x D   [0,1] Syntactic Module in a FG Set of Rules (Universe) DEGREE (ROL en el U) Syntactic Knowledge in FG:  M o [0,1] 

What is a Fuzzy Grammar? A Fuzzy Grammar (FGr) is a fuzzy set Which on the Cartesian product Which on the Cartesian product Of the set of the module’s rules. The rules define the Linguistic Knowdlege Of every module in a Fuzzy Grammar . Multi-Modal Fuzzy Grammar

How the linguistic modules are defined in a FGr? Set of syntactic Rules X  = {x   x  is a syntactic rule} The rules are extracted from a Grammar X: X  x D   [0,1] Syntax in FGr Set of Rules (Universe) DEGREE (ROL in U) Set of dialect rule D  = {d   d  is a dialect rule} These are obtained from the INPUT/OUTPUT

Defining the rules in each linguistic module Blache, 2016 The Constraints define the linguistic relation between POS and Syntax (or other Modules) and Syntax (or other Modules) Constraint behaviour in Fuzzy Constraint behaviour in Fuzzy Grammar Precedence A > B (  ) Canonical (Gold Standard) Requirement A  B Exclusion A  B (  ) Violated (  )Variability

PROPERTIES IN LINGUISTIC CONSTRUCTIONS CONSTRUCTION IS OUR FUZZY SET A Construction is Triggered by Each Category trigger a Set of Categories a Set of Properties PROPER NOUN NOMINAL PHRASE SUBJECT PROPN  DET DIRECT OBJECT MODIFICATOR PHRASE (Set of Properties of the PROPN) etc. Manchester vs El Manchester (?) PROPERTY GRAMMARS CONSTRUCTION= Set of Properties+ Set of Categories

PROPERTIES IN LINGUISTIC CONSTRUCTIONS LINGUISTIC CONSTRUCTION (Nominal Phrase) ADJ NOUN DET (red) (red) (car) (car) (the) (the) DET PROPERTIE’S ADJ NOUN PROPERTIE’S PROPERTIE’S DET > N DET dep . N N  DET ADJ > N DET agree N ADJ dep N DET  Pron, PROPN

“The book red” Initial Set :{Det1 N2 Adj3 } A= {{Det1 N2} {Det1 N2 Adj3}} A= {{Det1 N2} {Det1 N2 Adj3}} Assignation Properties {Det1 N2} P + = {Det<N; N  Det; Uniq (Det, N); Oblig (N)} P - = ∅ {Det1 N2 P + = {Det<N; N  Det; Uniq (Det, Adj3} N,Adj); Oblig (N) Adj mod N} P - = {Adj<N}

Example of a table of Linguistic Properties Constraint behaviour in Fuzzy Grammar (  ) Canonical (Gold Standard) (  ) Violated (  )Variability Transitivity Verb Construction In Spanish In Spanish Canonical (  ) Verb  dep Direct Object (N  PRON) Verb  dep Subject (N  PRON) Variability (  )  1 : V  S: S in verbal person (morpheme) FGr takes into account the VIOLATIONS but DOESN’T VIOLATE RULES

Extracting Constructions and Properties from Univ. Dep. & MarsaGram (17.000 treebanks aprox.): Linguistic Constructions & Properties

Why Dialect? Demonstration degrees of G/C in a FGr X: X   (D   M o ) Linguistic Knowledge in FG:  M o [0,1]  input input ACCEPTABILITY

Full Definition of a FGr X: X  x D   [0,1] X: X   (D   M o ) FGr   d   x  (X ( o  )  x  )d  Every Rule in a Dialect (D  ) triggers rules in a Module of a grammar (M  / X  ) , Both have a degree of Grammaticality

Example of association between sets and its Grammaticality Rule 1 , Rule 2 , Rule 3 , Rule 4  X  Is an example of rules that define the syntax of our FGr Rule a , Rule b , Rule c , Rule d  D  Is an example of rules that define an input in a Dialect X(Rule 1 , Rule a ) = 0.5 X(Rule 2 , Rule b ) = 0.8 X(Rule 2 , Rule b ) = 0.8 X(Rule 3 , Rule c ) = 0.6 X(Rule 4 , Rule c ) = 0.9 X(Rule 3 , Rule c ) = 0.6 & X(Rule 4 , Rule c ) = 0.9 They are an example of how a rule in an input of dialect can trigger two rules in the syntax rule set of a FGr (the canonical and the variable ) THE LESS GRAMMATICALITY THE MORE RULES ARE TRIGGERED

Value of Grammaticality First Parser Constraint behaviour in Fuzzy Grammar VG 1 =  +  (  ) Canonical (Gold  Standard) (  ) Violated (  ) Violated Second Parser Second Parser (  )Variability VG 2 = (  +  ) +  

Future Work…

FFI2015-69978-P, Ministerio de Economía y Competitividad: “ G RAMMATICAL I NFERENCE A LGORITHMS FOR MEASURING THE RELATIVE COMPLEXITY OF NATURAL LANGUAGE ”

adria.torrens@urv.cat