Lexicalized Tree-Adjoining Grammars (LTAG) - ad-teaching.infor...
Lexicalized Tree-Adjoining Grammars (LTAG) - ad-teaching.infor... Lexicalized Tree-Adjoining Grammars (LTAG) - ad-teaching.infor...
Recognizing Adjunction If we could traverse γ, we would follow the path · · · 1 ′′ · · · 2 ′′ · · · 3 ′′ · · · 4 ′′ · · · (1') (4') (1") (4") (1) (4) A A (α) A (β) (γ) (2) (3) w 1 w 5 A A w 1 w 3 w 5 w 2 w w 4 2 w 4 (2') (3') (2") (3") w 3 This can be simulated by traversing α and β such that the dots around the nodes labeled by A are visited in the following order: · · · 1 1 ′ · · · 2 ′ 2 · · · 3 3 ′ · · · 4 ′ · · · 4 · · · 32 / 52
Dotted Tree We introduce the notion of dotted tree. It consists of: a tree γ a dot location (adr, pos) where • adr is the Gorn address of a node in γ. • pos ∈ {la, lb, rb, ra} is a relative position. Definition (Gorn Address) Given a node n in a tree γ, the Gorn address of n is: 0, if n is the root k, if n is the k th child of the root adr.k, if n is the k th child of the node at address adr, adr ≠ 0 Start B A C End D (γ) E F G H I Example (Dotted trees) 〈γ, 0, la〉 ( • A ) 〈γ, 3, rb〉 ( D •) 〈γ, 2.1, ra〉 ( E • ) 33 / 52
- Page 1 and 2: Lexicalized Tree-Adjoining Grammars
- Page 3 and 4: Context-Free Grammars Definition (C
- Page 5 and 6: Tree-Substitution Grammars Example
- Page 7 and 8: Outline 1 Why CFGs are not enough (
- Page 9 and 10: Cross-Serial Dependencies Example (
- Page 11 and 12: Lexicalization Example (Lexicalized
- Page 13 and 14: Lexicalization Example (CFG which i
- Page 15 and 16: Outline 1 Why CFGs are not enough (
- Page 17 and 18: Initial Trees Definition (Initial T
- Page 19 and 20: Substitution Definition (Substituti
- Page 21 and 22: Adjunction Definition (Adjunction)
- Page 23 and 24: Adjunction Constraints Given TAG G
- Page 25 and 26: Lexicalization Example (strong lexi
- Page 27 and 28: Further Formal Properties of TAL Tr
- Page 29 and 30: TAG Parsing Parser: Given a string
- Page 31: Recognizing Adjunction But the algo
- Page 35 and 36: Chart Items The algorithm stores in
- Page 37 and 38: Scan Operations Input string: c 1
- Page 39 and 40: Complete Operations 1 2 3 [γ, adr,
- Page 41 and 42: Recognizer Algorithm Algorithm (Rec
- Page 43 and 44: Complexity of Recognizer Given: n:
- Page 45 and 46: Recognizing Substitution Recognizer
- Page 47 and 48: LTAG-Spinal Parser LTAG-spinal: Rou
- Page 49 and 50: LTAG-Spinal Parser Graphical repres
- Page 51 and 52: Conclusion TAG: a grammar formalism
Dotted <strong>Tree</strong><br />
We introduce the notion of dotted tree.<br />
It consists of:<br />
a tree γ<br />
a dot location (<strong>ad</strong>r, pos)<br />
where<br />
• <strong>ad</strong>r is the Gorn <strong>ad</strong>dress of<br />
a node in γ.<br />
• pos ∈ {la, lb, rb, ra} is a<br />
relative position.<br />
Definition (Gorn Address)<br />
Given a node n in a tree γ, the Gorn<br />
<strong>ad</strong>dress of n is:<br />
0, if n is the root<br />
k, if n is the k th child of the root<br />
<strong>ad</strong>r.k, if n is the k th child of the<br />
node at <strong>ad</strong>dress <strong>ad</strong>r, <strong>ad</strong>r ≠ 0<br />
Start<br />
B<br />
A<br />
C<br />
End<br />
D<br />
(γ)<br />
E F G H I<br />
Example (Dotted trees)<br />
〈γ, 0, la〉 ( • A )<br />
〈γ, 3, rb〉<br />
( D •)<br />
〈γ, 2.1, ra〉 ( E • )<br />
33 / 52
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