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Rajat Kumar Mohanty

AN INTRODUCTION TO

TREE ADJOINING GRAMMAR

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OUTLINE

• XTAG System• Basics of TAG Formalism• Operations• Constraints• Tree Families• Feature Structure

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2. XTAG SYSTEM

What does it do?It takes a sentence as input, and provides:• Constituency (NP, VP, PP, etc.) • Derivational History (how phrases are combined)• Predicate/ Argument Structure (main verb,

subject, object, etc)

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XTAG System: An Overview

Input Sentence

Morph Analyzer POS Tagger

POS Blender

Derivation Structure

Morph DB

Trees DB Syn DBTree Selection

Tree Grafting

Source: The XTAG Research Group, 2001

Stat. DB

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Diverse Linguistic Resources

• Subcategorization information (argument structure)

• Syntax of various constructions (specific transformations)

• Frequency information• Morphological information

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A Tree Adjoining Grammar (TAG) consists of a quintuple (, NT, I, A, S)

a. is a finite set of terminal symbols;b. NT is a finite set of non-terminal symbols:

NT = ;c. S is a distinguished non-terminal symbol: S

NT;d. I is a set of finite trees, called initial trees;e. A is a finite set of finite trees, called auxiliary

trees.

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I: Initial Tree

S alike

NP0 VP

V NP1

like

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A: Auxiliary Tree

S yesterday

Ad S*

yesterday

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Operations in Tree Adjoining Grammar

• SubstitutionThe substitution operation appends one tree at a frontier node of another tree. That is substitution takes place at non-terminal nodes on the frontier side, which are marked for substitution by a down arrow.

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Substitution

S asaw

NP0 VP

V NP1

saw

NP

aJohn

N

John

NP

aMary

N

Mary

S

NP0 VP

V NP1

N N

John saw Mary

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Adjunction

• The adjunction operation is more powerful.• It can be used to insert one tree within

another.• A new tree is built from an auxiliary tree

and a tree ( : initial, auxiliary or derived) by adjunction.

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Adjunction

S abought

NP0 VP

V NP1

bought

S

NP0 VP

V VP

has

V NP1

bought

has

VP

V VP*

has

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Adjoining Constraints

• Selective Adjunction: The adjunction of an auxiliary tree is not mandatory on the given node.

• Null Adjunction: It disallows any adjunction on the given node.

• Obligatory Adjunction: In this case, the adjunction of an auxiliary tree is mandatory.

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Derivation in Tree Adjoining Grammar

• Derived Tree

• Derivation Tree

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Derived Tree in TAG

S

Ad S

NP0 VP

N V NP1

N

Yesterday John saw Mary

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Derivation Tree in TAG

asaw

aJohn (1) aMary (2.2) yesterday (0)

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Declarative Intransitive Tree Family [Tnx0V]

Sr [ ] anx0V [ ]

NP0 [ ] VP [ ] [ ]

V< >

The intransitive verbs (e.g., sleep, dance, etc. )select this Tree family [Tnx0V].

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Ergative Tree Family [TEnx1V]

Sr [ ] anx1V [ ]

NP1 [ ] VP [ ] [ ]

V< > The ergative verbs (e.g., sink, melt, etc. )select this Tree family [Tnx1V].

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Sr [ ] anx0Vnx1

[ ]

NP0[] VP [ ]

[ ]

V< > NP1 [ ]

Declarative Transitive Tree Family [Tnx0Vnx1]

The transitive verbs (e.g., eat, like, hit, etc. )select this Tree family [Tnx0Vnx1]. e.g., I ate an apple.

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Declarative Ditransitive Tree Family [Tnx0Vnx1pnx2]

Sr [ ] anx0Vnx1pnx1 [ ]

  NP0 [ ] VP [ ]

[ ] 

V< > NP1 [ ] PP2 [ ]

The di-transitive verbs (e.g., put, usher, etc. )select this Tree family [Tnx0Vpnx1].

e.g.,The secretary ushered me into his office.

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This problem, I solved.   St [ ] [ ]

  NP1 [ ] Sr [ ] [ ]

NP0 [ ] VP[ ] [ ]

V< > NP1 [ ] NA

Transitive Tree with Object NP Extraction [aWnx1nx0Vnx1]

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What did he eat?   Sq [ ] [ ]

  NP1 [ ] Sr [ ] [ ]

NP0 [ ] VP[ ] [ ]

V< > NP1 [ ] NA

Transitive Tree with object Wh-NP Extraction [aWnx1nx0Vnx1]

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Sentential Complement Tree: [Tnx0Vnx1s2]

S r [ ] nx0Vnx1s2 [ ]

NP0[ ] VP [ ] [ ]

V<> NP1[ ] S2*[ ]

John told Mary that it was his turn.

John begged Mary to increase his disk quota.

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Complementizer Tree: [sCOMP] Sc [ ]

comp: <1> mode: <2> ind / inf    COMP [comp: <1> ] Sr* [assign-comp: <1>] [comp: <>]

mode: <2> comp: nil assign-comp: <>

John told Mary that it was his turn.

John begged Mary to increase his disk quota.

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Suggested Readings

• Joshi, A. K. 1987. An Introduction to Tree Adjoining Grammars. In A. Manaster-Ramer, ed., Mathematics of Language. Amsterdam: John Benjamins.

• XTAG Research Group. 1999. A Lexicalized Tree Adjoining Grammar for English. Technical Report IRCS, University of Pennsylvania, Philadelphia.