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

Stabler - Lx 185/209 2003
(37) Example. Consider again g5-mix.pl given in (32) above. There are infinitely many derivations of this
trivial result:
[n1] Rn1 [unreduce]
[n1] Rn1 [unreduce]
[n1] Rn1 [unreduce]
...
Nevertheless, the set of theorems, the set of pairs in the “is a beginning of” relation for the grammar
g5-mix.pl with the trigger relations indicated there, is finite.
We can compute the whole set by taking the closure of the axioms under the inference relation.
(38) Another wrinkle for the implementation: we store our beginnings in reversed, negated form, to make
it maximally easy to apply them in GLC reasoning.
¬qi,...,¬q1 nr R p [axiom-r] if p:-q1,...,qi ][q i+1,...,qn
¬qi,...,¬q1 nr R p [unscan-r] if qi ∈ Σ
¬qi−1,...,¬q1 nr R p
¬qi,...,¬q1 nr R p
¬rj,...,¬r1, ¬qi−1,...,¬q1 nr R p
[unreduce-r] if qi:-r1,...,rj ][r j+1,...,rn
(39) We will use code from Shieber, Schabes, and Pereira (1993) to compute the closure of these axioms
under the inference rules. 26
The following two files do what we want. (We have one version specialized for sicstus prolog, and one
for swiprolog.)
/* oracle-sics.pl
* E Stabler, Feb 2000
*/
:- op(1200,xfx,: ˜ ). % this is our object language "if"
:- [’closure-sics’]. % defines closure/2, uses inference/4
:- use_module(library(lists),[append/3,member/2]).
%verbose. % comment to reduce verbosity of chart construction
computeOracle :- abolish(nrR), setof(Axiom,axiomr(Axiom),Axioms), closure(Axioms, Chart), asserts(Chart).
axiomr(nrR(NRBA)) :- (A : ˜B+_), negreverse(B,[A|_],NRBA).
negreverse([],M,M).
negreverse([E|L],M,N) :- negreverse(L,[-E|M],N).
inference(unreduce-r/2,
[ nrR([-Qi|Qs]) ],
nrR(NewSeq),
[(Qi : ˜Prefix+_), negreverse(Prefix,[],NRPrefix),
append(NRPrefix,Qs,NewSeq) ]).
inference(unscan-r/2,
[ nrR([-Qi|Qs]) ],
nrR(Qs),
[ \+ (Qi : ˜_) ]).
asserts([]).
asserts([nrR([-C|Cs])|L]) :- !, assert(nrR([-C|Cs])), asserts(L).
asserts([_|L]) :- asserts(L).
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