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04/22/23 1
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.