The document discusses tree-adjoining grammars (TAG) as a mildly context-sensitive grammar formalism that can capture linguistic phenomena beyond context-free grammars while still allowing for polynomial time parsing. It introduces TAGs as consisting of elementary trees, which can be combined using substitution and adjunction operations. Examples are provided to illustrate how TAGs can be used to derive and parse sentences involving phenomena like wh-questions, relative clauses, light-verb constructions, and verb-particle constructions.

1. Natural Language Processing
Emory University
Jinho D. Choi
Tree-Adjoining
Grammar

2. Mildly Context-Sensitive Grammar
• Why another grammar?
- Context-free grammar cannot capture all linguistic phenomena.
- Context-sensitive grammar takes exponential time for parsing.
• Mildly context-sensitive grammar
- Can capture all linguistic phenomena in CFG and more.
- Can be parsed in polynomial time.
- Grows linearly as the string length grows.
• Formalisms
- Tree-adjoining grammars (TAG).
- Combinatory categorial grammars (CCG).
2

3. Tree-Adjoining Grammars
• Tree generating system
- What are the elementary objects of CFG?
- What are the elementary objects of TAG?
3
S, NP, VP, N, V, D,
I, bought, a, car
buy a car
ND
V
N
NP
VP
NP VP
will
V
S
buy
V NP1↓
VPNP0↓
S
car
ND↓
NP
a
D
VP*
VP
will
V
N
NP
← Strings ↑ Trees

4. Tree-Adjoining Grammars
• G = (N, Σ, S, I, A)
- N : a finite set of non-terminals.
- Σ : a finite set of terminals.
- S : a start symbol representing the whole sentence, where S ∈ N.
- I : a finite set of initial trees.
- A : a finite set of auxiliary trees.
4
Same as CFG
No production rules?
Substitution & Adjunction
Elementary trees

5. Elementary Tree
• Elementary trees (initial trees ∪ auxiliary trees)
- Interior nodes are labeled by non-terminals.
- Nodes on the frontier are labeled by terminals or non-terminals.
- Non-terminal nodes on the frontier are marked for substitution (↓).
• The foot node in an auxiliary tree is marked for adjunction (*).
• The foot node must have the same label as the root node.
5
VP*
VP
will
V
buy
V NP1↓
VPNP0↓
S
car
ND↓
NP
a
D
N
NP
Initial trees Auxiliary tree

6. Derivation
• Substitution
- Substitute X↓ with a tree whose root node is labeled by X.
- Only trees derived from initial trees can be substituted.
6
buy
V NP1↓
VPNP0↓
S
car
ND↓
NP
a
DN
NP
VP*
VP
will
V
car
ND
NP
a
Which NP?
car
ND
NP
a
V
VP
S
buy
N
NP

7. Derivation
• Adjunction
- Adjoin X* with a tree containing a non-substitution node labeled by X.
- Any adjunction on X↓ is not allowed.
7
car
ND
NP
a
V
VP
S
buy
N
NP VP*
VP
will
VVP
S
N
NP
N VP*
NP VP
will
V
S
car
ND
NP
a
V
VP
buy buy a car
ND
V
N
NP
VP
NP VP
will
V
S

8. Derivation Tree
• Derivation Tree
- Derived tree: a tree composed by two other trees.
- A tree showing how a derived tree was constructed.
8
buy
V NP1↓
VPNP0↓
S
αbuy
car
ND↓
NP
αcar
N
NP
αJohn
a
D
αa
VP*
VP
will
V
αwill
12
2.21
What kind of tree is this?

9. Lexicalization
• Lexicalized grammar
- A finite set of structures each associated with a lexical item (anchor).
- Operations composing the structures.
9
Design elementary trees using only substitutions
bought a car
ND
V
N
NP
VP
NP VP
almost
AP
S
A
by taking
1.The leftmost lexical item
2.The rightmost lexical item
3.The head lexical item
as the anchor of each phrase.

10. Lexicalization with Substitution
10
VP↓NP↓
S
N
VP↓
VP
almost
AP
A
bought
V NP↓
VP
a
N↓D
NP
car
N
Leftmost
lexical item
N
NP
almost
AP
A
bought
V
a
D
car
ND↓
V↓ NP
VP
NP↓ VP
AP↓
S
Rightmost
lexical item
bought
V NP↓
VP
NP↓ VP
AP↓
S
N
NP
almost
AP
A
car
ND↓
NP
a
D
Head
lexical item
Which gives the most meaningful trees?
Is this ideal?

11. Lexicalization with Adjunction
11
John bought a car John almost bought a car John bought a car too
bought
V NP↓
VP
S
NP↓
bought
V NP↓
VP
NP↓ VP
AP↓
S
bought
V NP↓
VP
NP↓
S
VP
AP↓
What should be included in the domain of locality for “bought”?
VP*
VP
A
AP
almost
AP
VP
A
VP*
toobought
V NP↓
VP
S
NP↓

12. Domain of Locality
• CFG vs TAG
- CFG, the domain of locality is constrained to direct children.
- TAG, the domain of locality can be extended much more.
• Reading presentation
- “Domain of Locality”,Aravind Joshi, 2004.
- Presented by Kate Silverstein.
• Next week’s readings
- “Synchronous Tree Adjoining Grammars”.
- Shieber & Schabes, 1990.
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13. Exercises
• Wh-question
- What did John buy for Mary
• Relative clause
- John bought a car which Mary wanted
• Light-verb construction
- John made a bid for the car
• Verb-particle construction
- Mary threw the car away
13

14. Wh-Question
14
V
NP VP
S
S
V
buy
NP
!
PP
P NP
for
N
Mary
N
Johndid
NP
S
N
What
“What did John buy for Mary”
V
NP↓ VP
S
S
NP↓
buy
NP
!
PP↓
NP
N
John
PP
P NP↓
for
S
V S*
did
NP
N
Wh
NP
N
Mary

15. Relative Clause
15
“John bought a car which Mary wanted”
a
D
bought
V NP↓
VP
S
NP↓
NP
N
John car
ND↓
NP NP
N
Mary NP↓ S
S
NP
NP*
NP↓ VP
V NP
!wanted
NP
N
which
NP S
S
NP
NP VP
V NP
!wanted
N
Mary
N
whicha
ND
NP
car
VP
V
bought
NP
John
N
S
Could it be adjoined earlier?

16. Light-Verb Construction
16
“John made a bid for the car”
made
V NP
VP
NP↓
S
VP
PP↓
D↓ N
bid
NP
N
John
PP
P NP↓
for car
ND↓
NP
a
D
the
D
made
V NP
VP
NP
S
VP
PP
D N
bid
P NP
for car
ND
theaJohn
N

17. Verb-Particle Construction
17
“Mary threw the car away”
threw
V NP↓
VP
S
NP↓
P
away
NP
N
Mary
the
D
car
ND↓
NP
threw
V NP
VP
S
NP
P
awayMary the car
N
ND