Notes on computational linguistics.pdf - UCLA Department of ...
Notes on computational linguistics.pdf - UCLA Department of ...
Notes on computational linguistics.pdf - UCLA Department of ...
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Stabler - Lx 185/209 2003<br />
7.1.2 CKY extended<br />
(5) We can relax the requirement that the grammar be in Chomsky normal form. For example, to allow<br />
arbitrary empty producti<strong>on</strong>s, and rules with right sides <strong>of</strong> length 3,4,5,6, we could add the following<br />
rules:<br />
(i, i) : A<br />
(i, j) : B (j,k) : C (k,l) : D<br />
(i, l) : A<br />
(i, j) : B (j,k) : C (k,l) : D (l,m) : E<br />
(i, m) : A<br />
(i, j) : B (j,k) : C (k,l) : D (l,m) : E (m,n) : F<br />
(i, n) : A<br />
(i, j) : B (j,k) : C (k,l) : D (l,m) : E (m,n) : F (n,o) : G<br />
(i, o) : A<br />
[reduce0] if A → ɛ<br />
[reduce3] if A → BCD<br />
[reduce4] if A → BCDE<br />
[reduce5] if A → BCDEF<br />
[reduce6] if A → BCDEFG<br />
(6) While this augmented parsing method is correct, it pays a price in efficiency. The Earley method <strong>of</strong> the<br />
next secti<strong>on</strong> can do better.<br />
(7) Using the strategy <strong>of</strong> computing closures (introduced in (39) <strong>on</strong> page 91), we can implement the CKY<br />
method with these extensi<strong>on</strong>s easily:<br />
/* ckySWI.pl<br />
* E Stabler, Feb 2000<br />
* CKY parser, augmented with rules for 3,4,5,6-tuples<br />
*/<br />
:- op(1200,xfx,:˜). % this is our object language "if"<br />
:- [’closure-swi’]. % Shieber et al’s definiti<strong>on</strong> <strong>of</strong> closure/2, uses inference/4<br />
%verbose. % comment to reduce verbosity <strong>of</strong> chart c<strong>on</strong>structi<strong>on</strong><br />
computeClosure(Input) :computeClosure(Input,Chart),<br />
nl,portray_clauses(Chart).<br />
/* ES tricky way to get the axioms from reduce0: */<br />
/* add them all right at the start */<br />
/* (there are more straightforward ways to do it but they are slower) */<br />
computeClosure(Input,Chart) :lexAxioms(0,Input,Axioms0),<br />
findall((Pos,Pos):A,(A :˜ []),Empties),<br />
append(Axioms0,Empties,Axioms),<br />
closure(Axioms, Chart).<br />
lexAxioms(_Pos,[],[]).<br />
lexAxioms(Pos,[W|Ws],[(Pos,Pos1):W|Axioms]) :-<br />
Pos1 is Pos+1,<br />
lexAxioms(Pos1,Ws,Axioms).<br />
inference(reduce1,<br />
[ (Pos,Pos1):W ],<br />
(Pos,Pos1):A,<br />
[(A :˜ [W])] ).<br />
inference(reduce2,<br />
[ (Pos,Pos1):B, (Pos1,Pos2):C],<br />
(Pos,Pos2):A,<br />
[(A :˜ [B,C])] ).<br />
/* reduce0 is here! */<br />
/* for efficiency, comment out the rules you never use */<br />
inference(reduce3,<br />
[ (Pos,Pos1):B, (Pos1,Pos2):C, (Pos2,Pos3):D],<br />
(Pos,Pos3):A,<br />
[(A :˜ [B,C,D])] ).<br />
inference(reduce4,<br />
[ (Pos,Pos1):B, (Pos1,Pos2):C, (Pos2,Pos3):D, (Pos3,Pos4):E],<br />
(Pos,A,Pos4),<br />
[(A :˜ [B,C,D,E])] ).<br />
inference(reduce5,<br />
[ (Pos,Pos1):B, (Pos1,Pos2):C, (Pos2,Pos3):D, (Pos3,Pos4):E, (Pos4,Pos5):F],<br />
(Pos,Pos5):A,<br />
[(A :˜ [B,C,D,E,F])] ).<br />
105
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