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

Stabler - Lx 185/209 2003
(8) Then we can have a session like this:
1 ?- [provable].
provable compiled, 0.00 sec, 1,432 bytes.
Yes
2 ?- (?˜ [p]).
Yes
3 ?- trace,(?˜ [p]).
Call: ( 7) ?˜[p] ?
Call: ( 8) infer([p], _L154) ?
Call: ( 9) p:˜_L168 ?
Exit: ( 9) p:˜[q, r] ?
Call: ( 9) append([q, r], [], _L154) ?
Call: ( 10) append([r], [], _G296) ?
Call: ( 11) append([], [], _G299) ?
Exit: ( 11) append([], [], []) ?
Exit: ( 10) append([r], [], [r]) ?
Exit: ( 9) append([q, r], [], [q, r]) ?
Exit: ( 8) infer([p], [q, r]) ?
Call: ( 8) ?˜[q, r] ?
Call: ( 9) infer([q, r], _L165) ?
Call: ( 10) q:˜_L179 ?
Exit: ( 10) q:˜[] ?
Call: ( 10) append([], [r], _L165) ?
Exit: ( 10) append([], [r], [r]) ?
Exit: ( 9) infer([q, r], [r]) ?
Call: ( 9) ?˜[r] ?
Call: ( 10) infer([r], _L176) ?
Call: ( 11) r:˜_L190 ?
Exit: ( 11) r:˜[] ?
Call: ( 11) append([], [], _L176) ?
Exit: ( 11) append([], [], []) ?
Exit: ( 10) infer([r], []) ?
Call: ( 10) ?˜[] ?
Exit: ( 10) ?˜[] ?
Exit: ( 9) ?˜[r] ?
Exit: ( 8) ?˜[q, r] ?
Exit: ( 7) ?˜[p] ?
Yes
2.2 A recognition predicate
(9) Now, we want to model recognizing that a string can be derived from ip in a grammar as finding a proof
of ip that uses the lexical axioms in that string exactly once each, in order.
To do this, we will separate the lexical rules Σ from the rest of our theory Γ that includes the grammar
rules. Σ is just the vocabulary of the grammar.
(10) The following proof system does what we want:
G, Γ ,S ⊢ G [axiom] for definite clauses Γ ,goalG, S ⊆ Σ∗ G, Γ ,S ⊢ (?-p, C)
G, Γ ,S ⊢ (?-q1,...,qn,C)
G, Γ ,wS ⊢ (?-w,C) [scan]
G, Γ ,S ⊢ (?-C)
28
if (p:-q1,...,qn) ∈ Γ