1. TREE ADJOINING GRAMMAR
AN INTRODUCTION TO
TREE ADJOINING GRAMMAR
Rajat Kumar Mohanty
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2. Basics of TAG Formalism Operations Constraints Tree Families
OUTLINE
XTAG System
Basics of TAG Formalism
Operations
Constraints
Tree Families
Feature Structure
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3. 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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4. XTAG System: An Overview
Input Sentence
Morph Analyzer
POS Tagger
Morph DB
Stat. DB
POS Blender
Trees DB
Syn DB
Tree Selection
Tree Grafting
Derivation Structure
Source: The XTAG Research Group, 2001
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5. Diverse Linguistic Resources
Subcategorization information (argument structure)
Syntax of various constructions (specific transformations)
Frequency information
Morphological information
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6. A Tree Adjoining Grammar (TAG) consists of a quintuple (, NT, I, A, S)
 is a finite set of terminal symbols;
NT is a finite set of non-terminal symbols:   NT = ;
S is a distinguished non-terminal symbol: S  NT;
I is a set of finite trees, called initial trees;
A is a finite set of finite trees, called auxiliary trees.
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7. I: Initial Tree
S like
NP0 VP
V NP1 
like
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8. A: Auxiliary Tree
S yesterday
Ad S*
yesterday
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9. Operations in Tree Adjoining Grammar
Substitution
The 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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10. Substitution NP John N John NP Mary N Mary S  NP0 VP V NP1 N N
John saw Mary
S saw
NP0 VP
V NP1 
saw
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11. 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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12. Adjunction S  NP0 VP V VP has V NP1 bought S bought NP0 VP
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13. 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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14. Derivation in Tree Adjoining Grammar
Derived Tree
Derivation Tree
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15. Derived Tree in TAG S  Ad S NP0 VP N V NP1 N Yesterday John saw Mary
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16. John (1) Mary (2.2) yesterday (0)
Derivation Tree in TAG
saw
John (1) Mary (2.2) yesterday (0)
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17. Declarative Intransitive Tree Family [Tnx0V]
Sr [ ] nx0V
[ ]
NP0 [ ] VP [ ]
V< >
The intransitive verbs (e.g., sleep, dance, etc. )select this Tree family [Tnx0V].
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18. Ergative Tree Family [TEnx1V]
Sr [ ] nx1V
[ ]
NP1 [ ] VP [ ]
V< >
The ergative verbs (e.g., sink, melt, etc. )select this Tree family [Tnx1V].
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19. Declarative Transitive Tree Family [Tnx0Vnx1]
Sr [ ] nx0Vnx1
[ ]
NP0[] VP [ ]
V< > NP1 [ ]
The transitive verbs (e.g., eat, like, hit, etc. )select this Tree family [Tnx0Vnx1]. e.g., I ate an apple.
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20. Declarative Ditransitive Tree Family [Tnx0Vnx1pnx2]
Sr [ ] nx0Vnx1pnx1
[ ]
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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21. Transitive Tree with Object NP Extraction [Wnx1nx0Vnx1]
This problem, I solved.  
St [ ]
[ ]
  NP1 [ ] Sr [ ]
NP0 [ ] VP[ ]
V< > NP1 [ ] NA 
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22. Transitive Tree with object Wh-NP Extraction [Wnx1nx0Vnx1]
What did he eat?  
Sq [ ]
[ ]
  NP1 [ ] Sr [ ]
NP0 [ ] VP[ ]
V< > NP1 [ ] NA 
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23. 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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24. Complementizer Tree: [sCOMP]
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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25. Suggested Readings
Joshi, A. K An Introduction to Tree Adjoining Grammars. In A. Manaster-Ramer, ed., Mathematics of Language. Amsterdam: John Benjamins.
XTAG Research Group A Lexicalized Tree Adjoining Grammar for English. Technical Report IRCS, University of Pennsylvania, Philadelphia.
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