Lexicalized Tree-Adjoining Grammars (LTAG) - ad-teaching.infor...
Lexicalized Tree-Adjoining Grammars (LTAG) - ad-teaching.infor... Lexicalized Tree-Adjoining Grammars (LTAG) - ad-teaching.infor...
Outline of the Algorithm Initialize the chart C with items of the form [α, 0, la, 0, −, −, 0, ⊥], where α ∈ I , root label S. Then use 4 types of operations to add new items to C: Scan, Predict, Complete, Adjoin Operations stated as inference rules: item 1 · · · item m item ∗ conditions Add item ∗ to C if item 1 ,· · ·, item m ∈ C and conditions are met. Accept input string c 1 · · · c n if C contains at least one item [α, 0, ra, 0, −, −, n, ⊥], where α ∈ I , root label S. 36 / 52
Scan Operations Input string: c 1 · · · c n Input TAG: G = (N, T , I , A, S) 1 [γ, adr, la, i, j, k, l, ⊥] [γ, adr, ra, i, j, k, l + 1, ⊥] γ(adr) ∈ T , γ(adr) = c l+1 a = c l + 1 a [i,j,k,l,⊥] a [i,j,k,l+1,⊥] 2 [γ, adr, la, i, j, k, l, ⊥] [γ, adr, ra, i, j, k, l, ⊥] γ(adr) = ε ε [i,j,k,l,⊥] ε [i,j,k,l,⊥] 37 / 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 and 32: Recognizing Adjunction But the algo
- Page 33 and 34: Dotted Tree We introduce the notion
- Page 35: Chart Items The algorithm stores in
- 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
Scan Operations<br />
Input string: c 1 · · · c n<br />
Input TAG: G = (N, T , I , A, S)<br />
1<br />
[γ, <strong>ad</strong>r, la, i, j, k, l, ⊥]<br />
[γ, <strong>ad</strong>r, ra, i, j, k, l + 1, ⊥]<br />
γ(<strong>ad</strong>r) ∈ T ,<br />
γ(<strong>ad</strong>r) = c l+1<br />
a = c l + 1<br />
a<br />
[i,j,k,l,⊥]<br />
a<br />
[i,j,k,l+1,⊥]<br />
2<br />
[γ, <strong>ad</strong>r, la, i, j, k, l, ⊥]<br />
[γ, <strong>ad</strong>r, ra, i, j, k, l, ⊥]<br />
γ(<strong>ad</strong>r) = ε<br />
ε<br />
[i,j,k,l,⊥]<br />
ε<br />
[i,j,k,l,⊥]<br />
37 / 52
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