Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
(33) GLC parsing with an oracle is defined so that whenever a completed category is placed on the stack,
the resulting sequence of completed categories on the stack must be a beginning of the most recently
predicted category.
Let’s say that a sequence C is reducible iff the sequence C is the concatenation of two sequences
C = C1C2 where
a. C1 is a sequence ¬pi,...,¬p1 of 0 ≤ i completed (i.e. negated) elements
b. C2 begins with a predicted (i.e. non-negated) element p, and
c. p1,...,pi is a beginning of p
(34) GLC parsing with an oracle:
G, Γ ,S ⊢ (?-¬qi,...,¬q1,C)
G, Γ ,S ⊢ (?-qi+1,...,qn, ¬p, C)
[glc]
if (p:-q1,...,qi][q i+1,...qn) ∈ Γ
and ¬p, C is reducible
G, Γ ,S ⊢ (?-¬qi,...,¬q1,p,C) [glc-complete] if (p:-q1,...,qi][q i+1,...qn) ∈ Γ
G, Γ ,S ⊢ (?-qi+1,...,qn,C)
G, Γ ,wS ⊢ (?-C)
G, Γ ,S ⊢ (?-¬w,C)
[shift] if ¬w,C is reducible
G, Γ ,wS ⊢ (?-w,C) [shift-complete] =scan
G, Γ ,S ⊢ (?-C)
(35) This scheme subsumes almost everything covered up to this point: Prolog is an instance of this scheme
in which every trigger is empty and the sequence of available “resources” is empty; LL, LR and LC are
obtained by setting the triggers at the left edge, right edge, and one symbol in, on the right side of each
rule.
(36) To implement GLC parsing with this oracle, we precalculate the beginnings of every category. In effect,
we want to find every theorem of the logic given above.
Notice that this kind of logic can allow infinitely many derivations.
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