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Adjoin Operation [β, 0, ra, i, j, k, l, ⊥] [γ, adr, rb, j, p, q, k, ⊥] [γ, adr, rb, i, p, q, l, ⊤] β ∈ SA(γ, adr) A A [i,j,k,l,⊥] + A [j,p,q,k,⊥] A [i,p,q,l,⊤] 40 / 52
Recognizer Algorithm Algorithm (Recognizer; Joshi and Schabes, 1997) Input: String c 1 · · · c n TAG G = (N, T , I , A, S) (that only allows adjunction) { } Initialize: C := [α, 0, la, 0, −, −, 0, ⊥] ∣ α ∈ I , α(0) = S While ( new items can be added to C ) apply the following operations on each item in C: [γ, adr, la, i, j, k, l, ⊥] [γ, adr, ra, i, j, k, l + 1, ⊥] [γ, adr, la, i, j, k, l, ⊥] [γ, adr, ra, i, j, k, l, ⊥] [γ, adr, la, i, j, k, l, ⊥] [β, 0, la, l, −, −, l, ⊥] [γ, adr, la, i, j, k, l, ⊥] [γ, adr, lb, l, −, −, l, ⊥] [β, adr, lb, l, −, −, l, ⊥] [γ, adr ′ , lb, l, −, −, l, ⊥] γ(adr) ∈ T , γ(adr) = c l+1 γ(adr) = ε γ(adr) ∈ N, β ∈ SA(γ, adr) γ(adr) ∈ N, OA(γ, adr) = ⊥ adr = foot(β), β ∈ SA(γ, adr ′ ) [γ, adr, rb, i, j, k, l, ⊥] [β, adr ′ , lb, i, −, −, i, ⊥] [β, adr ′ , rb, i, i, l, l, ⊥] [γ, adr, rb, i, j, k, l, adj] [γ, adr, la, h, −, −, i, ⊥] [γ, adr, ra, h, j, k, l, ⊥] [γ, adr, rb, i, −, −, l, adj] [γ, adr, la, h, j, k, i, ⊥] [γ, adr, ra, h, j, k, l, ⊥] [β, 0, ra, i, j, k, l, ⊥] [γ, adr, rb, j, p, q, k, ⊥] [γ, adr, rb, i, p, q, l, ⊤] Output: If ( ∃ [α, 0, ra, 0, −, −, n, ⊥] ∈ C : α ∈ I , α(0) = S ) then return acceptance else return rejection adr ′ = foot(β), β ∈ SA(γ, adr) γ(adr) ∈ N γ(adr) ∈ N β ∈ SA(γ, adr) 41 / 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 and 36: Chart Items The algorithm stores in
Page 37 and 38: Scan Operations Input string: c 1
Page 39: Complete Operations 1 2 3 [γ, adr,
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

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