组合范畴语法
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组合范畴语法. 孙薇薇 @ 计算机科学技术研究所 @ 北京大学. Outline. Local, Nonlocal TAG, HPSG, LFG Combinatory categorial grammar. Grammar formalisms and linguistic theories. Linguistics aims to explain natural language: What is universal grammar? What are language-specific constraints?

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组合范畴语法

孙薇薇@ [email protected]


Outline
Outline

  • Local, Nonlocal

  • TAG, HPSG, LFG

  • Combinatory categorial grammar


Grammar formalisms and linguistic theories
Grammar formalisms and linguistic theories

  • Linguistics aims to explain natural language:

    • What is universal grammar?

    • What are language-specific constraints?

  • Formalisms are mathematical theories:

    • They provide a language in which linguistic theories can be expressed (like calculus for physics)

    • They define elementary objects (trees, strings, feature structures) and recursive operationswhich generate complex objects from simple objects.

    • They do impose linguistic constraints (e.g. on the kinds of dependencies they can capture)


Lexicalized formalisms
Lexicalized formalisms

  • Lexicalized formalisms:

    • TAG, HPSG, LFG and CCG

  • The lexicon:

    • pairs words with elementary objects

    • specifies all language-specific information

  • The grammatical operations:

    • are universal

    • define (and impose constraints on) recursion


Tag hpsg lfg and ccg
TAG, HPSG, LFG and CCG

They describe different kinds of linguistic objects:

  • TAG: trees

  • LFG is a multi-level theory based on a projection architecture relating different types of linguistic objects

    • trees, feature structures, …

  • HPSG: typed feature structures

  • CCG: (syntactic and semantic) types


Lexicalized tree adjoining grammar
(Lexicalized) Tree-Adjoining Grammar

  • TAG is a tree-rewriting formalism:

    • TAG defines operations (substitution and adjunction) on trees.

    • The elementary objects in TAG are trees (not strings)

  • TAG is lexicalized:

    • Each elementary tree is anchored to a lexical item (word)

    • “Extended domain of locality”:The elementary tree contains all arguments of the anchor.

    • TAG requires a linguistic theory which specifies the shapeof these elementary trees.

  • TAG is mildly context-sensitive:

    • can capture Dutch crossing dependencies

    • but is still efficiently parseable


Tag substitution arguments

a1:

X

Y

X

Y

Substitute

Y

X

a3:

a2:

a1

a2

a3

TAG substitution (arguments)

Derived tree:

Derivation tree:


Tag adjunction modifiers

X

Auxiliary tree

Foot node

X*

X

X

X*

a1

b1

TAG adjunction (modifiers)

b1:

Derived tree:

a1:

ADJOIN

Derivation tree:


A small tag lexicon

a1:

S

NP

VP

NP

VBZ

eats

a2:

b1:

a3:

VP

NP

NP

VP*

RB

John

tapas

always

A small TAG lexicon


A tag derivation

NP

S

NP

John

NP

VP

a2

a3

tapas

NP

VBZ

eats

VP

VP*

RB

always

A TAG derivation

a1:

a1

NP

NP

b1:

a3:

a2:

NP

NP


A tag derivation1

S

NP

VP

VP

a2

a3

b1

NP

NP

VBZ

VBZ

eats

eats

tapas

VP

VP*

RB

always

A TAG derivation

a1

VP

John

tapas

S

NP

b1

VP

VP

VP*

RB

John

always


Head driven phrase structure grammar hpsg
Head-Driven Phrase Structure Grammar (HPSG)

  • HPSG is a unification-/constraint-based theory of grammar

  • Syntactic/semantic constraints are uniformly denoted by signs, which are represented with feature structures

  • Two components of HPSG

    • Lexical entries represent word-specific constraints

      • elementary objects

    • Principles express generic grammatical regularities

      • grammatical operations


Sign

  • Sign is a formal representation of combinations of phonological forms, syntactic and semantic constraints

phonological form

signPHON string

syntactic/semanticconstraints

synsem

local constraints

local

category

syntactic category

head

MOD synsem

HEAD

CAT

syntactic head

valence

SPR listSUBJ list

COMPS list

SYNSEM

LOCAL

VAL

modifying constraints

subcategorization frames

CONT content

nonlocal

QUE listREL list

SLASH list

semantic representations

NONLOCAL

non-local dependencies

DTRS dtrs

daughter structures


Lexical entries
Lexical entries

  • Lexical entries express word-specific constraints


Principles
Principles

  • Principles describe generic regularities of grammar

    • Not corresponding to construction rules

  • Head Feature Principle

    • The value of HEAD must be percolated from the head daughter

  • Valence Principle

    • Subcats not consumed are percolated to the mother

  • Immediate Dominance (ID) Principle

    • A mother and her immediate daughters must satisfy one of ID schemas

  • Many other principles: percolation of NONLOCAL features, semantics construction, etc.


Syntactic structure
Syntactic Structure

  • Lexical entries determine syntactic/semantic constraints of words

Lexical entries

HEAD nounSUBJ <>COMPS <>

HEAD verbSUBJ <HEAD noun>COMPS <HEAD noun>

HEAD nounSUBJ <>COMPS <>

John

saw

Mary


Syntactic structure1
Syntactic Structure

  • Principles determine generic constraints of grammar

HEAD SUBJCOMPS

1

2

4

HEAD SUBJCOMPS < | >

1

Unification

3

2

3

4

HEAD nounSUBJ <>COMPS <>

HEAD verbSUBJ <HEAD noun>COMPS <HEAD noun>

HEAD nounSUBJ <>COMPS <>

John

saw

Mary


Syntactic structure2
Syntactic Structure

  • Principle application produces phrasal signs

HEAD verbSUBJ <HEAD noun>COMPS <>

HEAD nounSUBJ <>COMPS <>

HEAD verbSUBJ <HEAD noun>COMPS <HEAD noun>

HEAD nounSUBJ <>COMPS <>

John

saw

Mary


Syntactic structure3
Syntactic Structure

  • Recursive applications of principles

HEAD verbSUBJ <>COMPS <>

HEAD verbSUBJ <HEAD noun>COMPS <>

HEAD nounSUBJ <>COMPS <>

HEAD verbSUBJ <HEAD noun>COMPS <HEAD noun>

HEAD nounSUBJ <>COMPS <>

John

saw

Mary


Lexical functional grammar lfg
Lexical-Functional Grammar (LFG)

Two (basic) levels of representation:

  • C-structure: represents surface syntactic configurations

    • word order, annotated phrase-structures

    • trees

  • F-structure: represents abstract grammatical functions

    • SUBJ, OBJ, OBL, PRED, COMP, ADJ, …

    • AVM

  • F-structure approximates to basic predicate-argument structure, dependency representation






Outline1
Outline

  • Local, Nonlocal

  • TAG, HPSG, LFG

  • Combinatory categorial grammar


Motivation for c cg
Motivation for (C)CG

  • Only a “minimal” extension to CFGs → formalism is also well-understood from a logical standpoint

  • Transparent interface to (compositional) semantics

  • Cross-linguistic generalizations can be made easily

    • the same set of rules always apply

  • Flexible constituency


Combinatory categorial grammar
Combinatory Categorial Grammar

  • Categories: specify subcat lists of words/constituents.

  • Combinatory rules: specify how constituents can combine.

  • The lexicon: specifies which categories a word can have.

  • Derivations: spell out process of combining constituents.


Ccg categories
CCG categories

  • Simple categories:NP, S, PP

  • Complex categories: functions which return a result when combined with an argument:

    VP or intransitive verb: S\NPTransitive verb: (S\NP)/NPAdverb: (S\NP)\(S\NP)PPs: ((S\NP)\(S\NP))/NP(NP\NP)/NP

  • Every category has a semantic interpretation


The combinatory rules
The combinatory rules

  • Function application: x.f(x) a  f(a)

    X/YY X (>)

    Y X\Y  X (<)

  • Function composition: x.f(x) y.g(y)  x.f(g(x))

    X/Y Y/Z X/Z(>B)

    Y\Z X\Y  X/Z(<B)

    X/YY\Z X\Z(>Bx)

    Y/Z X\Y  X/Z(<Bx)

  • Type-raising: a f.f(a)

    X T/(T\X) (>T)

    X T\(T/X) (<T)


Function application
Function application

  • Combines a function with its argument to yield aresult:(S\NP)/NP NP -> S\NPeats tapas eats tapasNPS\NP -> SJohn eats tapas John eats tapas

  • Used in all variants of categorial grammar


A c cg derivation
A (C)CG derivation


Type raising and function composition
Type-raising and function composition

  • Type-raising: turns an argument into a function.Corresponds to case: NP -> S/(S\NP) (nominative)NP -> (S\NP)/((S\NP)/NP) (accusative)

  • Function composition: composes two functions (complex categories)(S\NP)/PP PP/NP -> (S\NP)/NPS/(S\NP) (S\NP)/NP -> S/NP


Type raising and composition
Type-raising and Composition

  • Wh-movement:

  • Right-node raising:



Ccg semantics
CCG: semantics

  • Every syntactic categoryand rule has a semantic counterpart:


The ccg lexicon
The CCG lexicon

  • Pairs words with their syntactic categories(and semantic interpretation):

    eats (S\NP)/NPxy.eats’xyS\NPx.eats’x

  • The main bottleneck for wide-coverage CCG parsing







Summary
Summary

  • CCG is a lexicalized grammar formalism

    • “rules” of are extremely general, just like HPSG schemata

  • CCG is nearly context-free

    • Weakly equivalent to TAG

  • CCG has a flexible constituent structure

  • CCG has a transparent syntax-semantics interface

    • Every syntactic category and combinatory rule has a semantic interpretation

  • Movement or traces don’t exist

  • CCG rules are type-driven, not structure-driven

    • E.g. intransitive verbs and VPs are indistinguishable