Lattice, Université Paris 7

Lattice, Université Paris 7
What is a Natural Language and How to Describe It? Meaning-Text Approaches in contrast with Generative Approaches Sylvain Kahane Lattice, Université Paris 7 Mexico, February 19-24, 2001

Sylvain Kahane, Mexico, February 2001
Meaning-Text Theory Foundation: research in Machine Translation in Moscow (Zolkovskij & Mel'cuk 1965, 1967) Main references: Mel'cuk, 1988, Dependency Syntax: Theory and Practice, SUNY Press Mel'cuk et al. 1984, 1988, 1992, 1999, Dictionnaire explicatif et combinatoire du français contemporain, Vol. 1, 2, 3, 4. Mel'cuk, , Cours de morphologie générale, 5 vol. Sylvain Kahane, Mexico, February 2001

Contents 1. MTT's Postulates 2. MTT's Representations 3. Correspondence Modules 4. Comparison with Generative/Unification Grammars Sylvain Kahane, Mexico, February 2001

1. MTT's Postulates Sylvain Kahane, Mexico, February 2001

First postulate Postulate 1 Natural language is (considered as) a many-to-many correspondence between meanings and texts { meanings } { texts } natural language Sylvain Kahane, Mexico, February 2001

Many-to-many correspondence
{ meanings } { texts } 1 2 ‘cause’ ‘Peter’ ‘Mary’ ‘leave’ ‘cry’ Mary's leaving caused Peter to cry Mary's departure makes Peter cry Peter cried because Mary left Mary left. Peter cried. …. …. Sylvain Kahane, Mexico, February 2001

Comparison with Chomsky 1957 (1)
Chomsky 1957: description of a natural language L = description of the set of acceptable sentences of L Formal language = set of strings A natural language can never be modeled by a formal language in this sense Sylvain Kahane, Mexico, February 2001

Comparison with Chomsky 1957 (2)
a sentence is not a string a sentence is a sign with a meaning (signifié) and a form (signifiant) correspondence between two sets A and B = a set of couples of two corresponding elements correspondence between meanings and texts = set of couples of a meaning and a corresponding text = set of sentences Sylvain Kahane, Mexico, February 2001

Second postulate Postulate 2 The Meaning-Text correspondence is described by a formal device which simulates the linguistic activity of native speaker A speaker speaks = transforms what he wants to say (a meaning) into what he says (a text) The correspondence is bidirectional but the direction from meanings to texts must be privilegiated Grammar rules = correspondence rules Sylvain Kahane, Mexico, February 2001

Third postulate Postulate 3 Intermediate levels of representation have to be distinguished: a syntactic and a morphological level (sentences' and words' organisation) { SemR } { PhonR } { SyntR } { MorphR } semantics syntax morphology Sylvain Kahane, Mexico, February 2001

Modularity The correspondence is completely modular Semantics, syntax and morphology are three correspondence modules semantics { SyntR } { MorphR } { SemR } { PhonR } syntax morphology Sylvain Kahane, Mexico, February 2001

Modularity No primacy of syntax A well-formed SyntR is only characterized by the fact that it is a possible intermediary between a SemR and a PhonR It is not the aim of MTT to give explicit characterization of well-formed SyntR semantics { SyntR } { MorphR } { SemR } { PhonR } syntax morphology Sylvain Kahane, Mexico, February 2001

Conclusion of Part 1 MTT's postulates are more or less accepted by the whole linguistic community The first sentences of MP's presentation of Brody1995: "It is a truism that grammar relates sound and meaning. Theories that account for this relationship with reasonable success postulate representation levels corresponding to sound and meaning and assume that the relationship is mediated through complex representations that are composed of smaller units." Main difference of view: describe a natural language as a correspondence Sylvain Kahane, Mexico, February 2001

2. MTT's Representations Sylvain Kahane, Mexico, February 2001

Geometry SemR = graph of predicate-argument relations SyntR = dependency tree MorphR = string of words PhonR = string of phonems ® Semantic module: hierarchization ® Syntactic module: linearization Sylvain Kahane, Mexico, February 2001

Semantic representation
The core of the semantic representation is a directed graph whose nodes are labeled by semantemes lexical semantemes = meanings of words or idioms grammatical semantemes = meanings of grammatical inflections Arrows = predicate-argument relations = semantic dependencies Sylvain Kahane, Mexico, February 2001

Graphs and logical formula
x,y,p,s,e,m ‘Peter’(x) ‘car’(y) ‘blue’(p,y) ‘belong’(s,y,x) ‘sell’(e,x,y) ‘want’(m,x,e) m e x s y p 1 2 ‘want’ ‘car’ ‘belong’ ‘Peter’ ‘blue’ ‘sell’ Peter wants to sell his blue car Sylvain Kahane, Mexico, February 2001

Communicative structure
Rheme-theme partition rheme = what we say theme = what we are talking about Area + communicatively dominant node R LAST 1 2 ‘last’ ‘Mary’ ‘2 hours’ ‘nap’ subj comp det MARY 2 HOURS NAP T Mary's nap lasted 2 hours Sylvain Kahane, Mexico, February 2001

Communicative structure
Rheme-theme partition rheme = what we say theme = what we are talking about Area + communicatively dominant node NAP R 1 2 ‘last’ ‘Mary’ ‘2 hours’ ‘nap’ subj circ prep MARY 2 HOURS DURING T Mary naped during 2 hours Sylvain Kahane, Mexico, February 2001

Comm. structure and relatives
‘read’ ‘buy’ ‘man’ 1 2 ‘book’ Kahane & Mel'cuk 1999 A man read a book that he bought A man bought a book that he read A man that bought a book read it R R T ‘read’ ‘buy’ ‘man’ 1 2 ‘book’ ‘read’ ‘buy’ ‘man’ 1 2 ‘book’ T Sylvain Kahane, Mexico, February 2001

Syntactic representation
The core of the syntactic representation is non ordered dependency tree whose nodes are labeled by lexical units (+ grammemes) whose branches are labeled by syntactic relations Sylvain Kahane, Mexico, February 2001

Dependency tree vs. Phrase structure tree
det mod A BLUE LOOK subj comp prep MARY CAR FOR sg ind,pres NP VP N V PP Mary looks P NP for D Adj N a blue car Mary looks for a blue car Sylvain Kahane, Mexico, February 2001

Dependency tree vs. Phrase structure tree
Our dependency tree is non ordered Mary looks for a blue car det mod A BLUE LOOK subj comp prep MARY CAR FOR sg ind,pres S VP NP N Mary V looks PP P for Adj D a blue car Sylvain Kahane, Mexico, February 2001

Morphological representation
The core of the morphological representation is the string of the morphological representation of the words Morphological representation of a word = lemma + string of grammemes (including agreement and government grammemes) MARY LOOK FOR A BLUE CAR ind,present sg ,3,sg Prosodic structure Sylvain Kahane, Mexico, February 2001

3. Correspondence Modules Sylvain Kahane, Mexico, February 2001

General articulation morphological module semantic module syntactic module { SemR } { PhonR } { SyntR } { MorphR } hierarchization lexicalization pronominalization linearization agreement prosody morphologisation phonologisation Sylvain Kahane, Mexico, February 2001

Semantic module Hierarchization: Choose the root of the tree T R i ‘X’ ‘Y’ X subj Y (V) Sylvain Kahane, Mexico, February 2001

Semantic module LAST subj comp X Y (V) Lexicalization 1 2 ‘last’ ‘Y’ ‘X’ circ prep DURING (Prep) X Y (V) (N) Sylvain Kahane, Mexico, February 2001

Semantic module Lexicalization X (V) (N) suj NAP ‘X’ 1 ‘nap’ X (N) det NAP Sylvain Kahane, Mexico, February 2001

Semantic module: Synthesis
R 1 2 ‘last’ ‘Mary’ ‘2 hours’ ‘nap’ Mary naped during 2 hours Sylvain Kahane, Mexico, February 2001

Semantic module: Synthesis
NAP R 1 2 ‘last’ subj (V) circ prep DURING (Prep) ‘nap’ 1 MARY (N) ‘2 hours’ T 2 HOURS (N) ‘Mary’ Mary naped during 2 hours Sylvain Kahane, Mexico, February 2001

Semantic module: Analysis
NAP subj (V) circ prep DURING (Prep) 2 HOURS (N) MARY Mary naped during 2 hours Sylvain Kahane, Mexico, February 2001

Semantic module: Analysis
NAP subj (V) T R 1 2 ‘last’ circ prep DURING (Prep) 1 ‘nap’ MARY (N) ‘2 hours’ 2 HOURS (N) ‘Mary’ Mary naped during 2 hours Sylvain Kahane, Mexico, February 2001

Syntactic module Linearization subj X Y (V) (N) Y < X d(X,Y) = -10 Sylvain Kahane, Mexico, February 2001

Syntactic module Linearization adv X Y (V) Y < X d(X,Y) = -5 (Adv) Sylvain Kahane, Mexico, February 2001

Syntactic module Agreement subj X Y (V) (N)n X (V)3,n Sylvain Kahane, Mexico, February 2001

Syntactic module: Synthesis (N)pl subj EAT (V) obj mod BEAN RED (Adj) PETER (N)sg adv OFTEN (Adv) Peter often eats red beans Sylvain Kahane, Mexico, February 2001

Syntactic module: Synthesis EAT (V) -10 subj PETER (N)sg obj +10 BEAN (N)pl subj PETER (N)sg adv OFTEN (Adv) obj BEAN (N)pl -5 adv OFTEN (Adv) -5 mod RED (Adj) mod RED (Adj) EAT (V) 3,sg Peter often eats red beans Sylvain Kahane, Mexico, February 2001

Syntactic module: Synthesis EAT (V) subj PETER (N)sg adv OFTEN (Adv) obj BEAN (N)pl mod RED (Adj) PETER OFTEN EAT RED BEAN (N)sg (Adv) (V) 3,sg (Adj) (N)pl Peter often eats red beans Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Global analysis (CKY) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg Peter often eats red beans Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Global analysis EAT (V) obj BEAN (N)pl mod RED (Adj) subj PETER (N)sg adv OFTEN (Adv) EAT (V) obj +10 BEAN (N)pl -5 adv OFTEN (Adv) -5 mod RED (Adj) -10 subj PETER (N)sg 3,sg Peter often eats red beans Sylvain Kahane, Mexico, February 2001

Projectivity Lecerf 1961, Iordanskaja 1963, Gladkij 1966 An ordered dependency tree is projective iff: No dependencies cross each other No dependency covers the root * Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg Peter often eats red beans Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) PETER (N)sg EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg Peter often eats red beans [N ,-,1] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) PETER (N)sg OFTEN (Adv) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg [Adv,-,2] Peter often eats red beans [N ,-,1] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) PETER (N)sg OFTEN (Adv) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg [V ,-,3] [Adv,-,2] Peter often eats red beans [N ,-,1] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) adv PETER (N)sg OFTEN (Adv) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg [N ,-,1] [V ,-,3] Peter often eats red beans Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) subj adv PETER (N)sg OFTEN (Adv) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg Peter often eats red beans [V ,-,3] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) subj adv PETER (N)sg OFTEN (Adv) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg RED (Adj) [Adj,-,4] Peter often eats red beans [V ,-,3] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) subj adv PETER (N)sg BEAN (N)pl OFTEN (Adv) EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg RED (Adj) [N ,-,5] [Adj,-,4] Peter often eats red beans [V ,-,3] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) subj adv EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg PETER (N)sg BEAN (N)pl OFTEN (Adv) mod RED (Adj) [N ,-,5] Peter often eats red beans [V ,-,3] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) subj adv obj EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg PETER (N)sg BEAN (N)pl OFTEN (Adv) mod RED (Adj) [N ,+,5] Peter often eats red beans [V ,-,3] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) EAT (V) subj adv obj PETER (N)sg BEAN (N)pl OFTEN (Adv) mod PETER OFTEN EAT RED BEAN RED (Adj) (N)sg (Adv) (V) 3,sg (Adj) (N)pl Peter often eats red beans [V ,-,3] Sylvain Kahane, Mexico, February 2001

Syntactic module: Analysis Incremental analysis (stack automaton) The stack automaton have four types of transitions Stacking transition: read a node, stack it and produce it Linking transition: produce a dependency Negative weight (governor on the right): remove the second slot of the stack Positive weight (governor on the left): indicate that the first slot is governed Removing transition: remove the first slot if it is governed Sylvain Kahane, Mexico, February 2001

Flow and complexity Flow = number of dependencies linking a word on the left with a word on the right The flow of natural languages is bounded (memorial limitations) ® The number of slots in the stack is bounded ® The number of stack contents is finite ® Equivalence with a finite state automaton ® Linear-time analysis Sylvain Kahane, Mexico, February 2001

4. Comparison with Generative/Unification Grammars Sylvain Kahane, Mexico, February 2001

MTT module and correspondence
An MTT module defines more than a correspondence between two sets of structures Sylvain Kahane, Mexico, February 2001

Product structure tree map linearly ordered tree = product of a tree
(N)pl subj EAT (V) obj mod BEAN RED (Adj) PETER (N)sg adv OFTEN (Adv) EAT (V) obj BEAN (N)pl adv OFTEN (Adv) mod RED (Adj) subj PETER (N)sg 3,sg map linearly ordered tree = product of a tree and a linear order EAT (V) BEAN (N)pl OFTEN (Adv) RED (Adj) PETER (N)sg 3,sg string (= linear order) Sylvain Kahane, Mexico, February 2001

Supercorrespondence An MTT module defines a supercorrespondence between two sets of structure, that is, a correspondence and for each couple of structures in correspondence a map between some pieces of the structures For instance, the syntactic module defines a supercorrespondence between trees and strings, that is, a correspondence and for each couple of a tree and a string in correspondence a map between their nodes Sylvain Kahane, Mexico, February 2001

Let's come back to the first postulate
Postulate 1 (revised) Natural language is (considered as) a many-to-many supercorrespondence between meanings and texts Sentence = product structure map between pieces of meaning and pieces of texts (compositionality) Sylvain Kahane, Mexico, February 2001

MTT modules as generative grammars
A correspondence between A and B is equivalent to a set of couples (S,S') with S in A and S' in B A supercorrespondence is equivalent to a set of product structures, that is, triples (S,S',ƒ) with S in A, S' in B and ƒ a map between some partitions of S and S' An MTT module defines a supercorrespondence; this can be done by generating the set of product structures Sylvain Kahane, Mexico, February 2001

Syntactic rules as generative rules
subj X Y (V) -10 subj (V) (N) Y < X d(X,Y) = -10 (N) Sylvain Kahane, Mexico, February 2001

Derivation -5 adv (V) (Adv) Generate a set of rules -10 subj (V) (N) EAT (V) obj BEAN (N)pl adv OFTEN (Adv) mod RED (Adj) subj PETER (N)sg 3,sg -5 mod (N) (Adj) +10 obj (N) (V) EAT (V) 3,sg PETER (N)sg BEAN (N)pl Combine them by unification OFTEN (Adv) RED (Adj) Sylvain Kahane, Mexico, February 2001

Semantic rules as generative rules
EAT (V) sem: ‘eat’ arg1: x arg2: y subj obj (N) sem: x sem: y 1 2 ‘eat’ ‘Y’ ‘X’ EAT subj obj X Y (V) (N) Sylvain Kahane, Mexico, February 2001

Derivation BEAN (N) sem: ‘bean’ Generate a set of rules mod RED (Adj) sem: ‘red’ arg1: x (N) sem: x EAT (V) sem: ‘eat’ arg1: x arg2: y subj obj (N) sem: x sem: y Combine them by unification adv OFTEN (Adv) sem: ‘often’ arg1: x (V) sem: x PETER (N) sem: ‘Peter’ Sylvain Kahane, Mexico, February 2001

Derivation EAT (V) sem: ‘eat’ arg1 : ‘Peter’ arg2 : ‘bean’ subj obj BEAN (N) sem: ‘bean’ PETER sem: ‘Peter’ mod RED (Adj) sem: ‘red’ arg1 : ‘bean’ adv OFTEN (Adv) sem: ‘often’ arg1 : ‘eat’ Generate a set of rules Combine them by unification Sylvain Kahane, Mexico, February 2001

Product structure ‘red’ (N)pl subj EAT (V)ind,present obj mod BEAN RED (Adj) PETER (N)sg adv OFTEN (Adv) 1 2 ‘eat’ ‘often’ ‘bean’ ‘Peter’ EAT (V)ind,present sem: ‘eat’ arg1 : ‘Peter’ arg2 : ‘bean’ subj obj BEAN (N)pl sem: ‘bean’ PETER (N)sg sem: ‘Peter’ mod RED (Adj) sem: ‘red’ arg1 : ‘bean’ adv OFTEN (Adv) sem: ‘often’ arg1 : ‘eat’ Sylvain Kahane, Mexico, February 2001

Morphological rules as generatives rules
eats (written) /i:ts/ (speech) EAT (V)ind,present,3,sg EAT (V)ind,present,3,sg graph: eats phon: /i:ts/ Sylvain Kahane, Mexico, February 2001

Combination of modules
Sylvain Kahane, Mexico, February 2001

semantic representation
EAT (V)present sem: ‘eat’ arg1: x arg2: y subj obj (N) sem: x sem: y PETER (N)sg sem: ‘Peter’ adv OFTEN (Adv) sem: ‘often’ arg1: x (V) sem: x mod RED (Adj) sem: ‘red’ arg1: x (N) sem: x BEAN (N)pl sem: ‘bean’ syntactic representation (V)t,3,n -5 adv -10 subj +10 obj -5 mod subj (Adv) (V) (N) (V) (V) (N) (Adj) (N) (N)n morphological representation PETER (N)sg graph: Peter phon: /pi:te*/ OFTEN (Adv) graph: often phon: /ofn/ EAT (V)ind,present,3,sg graph: eats phon: /i:ts/ RED (Adj) graph: red phon: /red/ BEAN (N)pl graph: beans phon: /bi:ns/ graphic/phonological representation Sylvain Kahane, Mexico, February 2001

Analysis Two main strategies: Horizontal analysis (module after module): tagging, shallow parsing, deep analysis Vertical analysis (word after word): lexicalization Sylvain Kahane, Mexico, February 2001

Horizontal analysis semantic representation deep analysis
(V) (N) (Adj) (Adv) (V)t,3,n (N)n EAT (V)present sem: ‘eat’ arg1: x arg2: y subj obj sem: x sem: y mod RED sem: ‘red’ adv OFTEN sem: ‘often’ BEAN (N)pl sem: ‘bean’ PETER (N)sg sem: ‘Peter’ -10 subj -5 adv -5 mod +10 obj (V)ind,present,3,sg graph: eats phon: /i:ts/ graph: Peter phon: /pi:te*/ graph: beans phon: /bi:ns/ graph: often phon: /ofn/ graph: red phon: /red/ semantic representation syntactic representation morphological representation graphic/phonological representation deep analysis shallow parsing tagging Sylvain Kahane, Mexico, February 2001

Vertical analysis semantic representation syntactic representation
(Adj) (Adv) (V)t,3,n (N)n EAT (V)present sem: ‘eat’ arg1: x arg2: y subj obj sem: x sem: y mod RED sem: ‘red’ adv OFTEN sem: ‘often’ BEAN (N)pl sem: ‘bean’ PETER (N)sg sem: ‘Peter’ -10 subj -5 adv -5 mod +10 obj (V)ind,present,3,sg graph: eats phon: /i:ts/ graph: Peter phon: /pi:te*/ graph: beans phon: /bi:ns/ graph: often phon: /ofn/ graph: red phon: /red/ semantic representation syntactic representation morphological representation graphic/phonological representation Sylvain Kahane, Mexico, February 2001

Lexicalization (V) (N) (V)t,3,n (N)n EAT (V)present sem: ‘eat’ arg1: x arg2: y subj obj sem: x sem: y -10 subj +10 obj (V)ind,present,3,sg graph: eats phon: /i:ts/ Sylvain Kahane, Mexico, February 2001

Lexicalization (V) (N) (V)t,3,n (N)n EAT (V)present sem: ‘eat’ arg1: x arg2: y subj obj sem: x sem: y -10 subj +10 obj (V)ind,present,3,sg graph: eats phon: /i:ts/ EAT (V)present,3,sg sem: ‘eat’ arg1: x arg2: y graph: eats phon: /i:ts/ -10 subj obj +10 (N)sg sem: x (N) sem: y Sylvain Kahane, Mexico, February 2001

Let's go to my first talk: A Fully lexicalized Grammar based on the Meaning-Text Theory How to lexicalize a modular grammar? = How to group the rules of the modular grammar? (which of two words must "decide" their relative positioning? Which word must "decide" to the distribution of a phrase?…) Sylvain Kahane, Mexico, February 2001

Conclusion MTT provides a clear separation of semantic, syntactic and morphological information (modular grammar) Comparison between correspondence grammars and generative grammars: Linguistics needs grammars that generate product structures and define (super)correspondences Two grammars are strongly equivalent iff they define the same (super)correspondence Sylvain Kahane, Mexico, February 2001

Conclusion Get a fully lexicalized grammar from a modular grammar (Vijay-Shanker 1992, Kasper et al. 1995, Candito 1996 …) Advantage: we write a modular and a fully lexicalized grammar in the same formalism ® lexicalization in several ways ® partially lexicalized grammars Cognitive viewpoint: the modularity of the grammar does not imply that synthesis or analysis are process module after module Strategies between horizontal and vertical strategies Sylvain Kahane, Mexico, February 2001

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