1. Vlado Keselj UW Math Grad Conference 2001 slide 1 Just-in-time Subgrammar Extraction for HPSG Vlado Keselj Graduate Student Conference Faculty of Mathematics University of Waterloo June 26, 2001

2. Vlado Keselj UW Math Grad Conference 2001 slide 2 What is "just-in-time subgrammar extraction” NL grammar subgrammar extraction subgrammar parser NL text =========== parsing results

3. Vlado Keselj UW Math Grad Conference 2001 slide 3 Motivation 1 managing complexity 2 parsing efficiency 3 context-based disambiguation * Subgrammar extraction is defined within the framework of grammar modularity.

4. Vlado Keselj UW Math Grad Conference 2001 slide 4 Subgrammar Definition Sentence: Grammar: Subgrammar: any partial order: G 1  G 2 such that: G 1  G 2 implies s   * G(s)={(s,p 1 ),…,(s,p n )}  s  * G 1 (s)  G 2 (s)

5. Vlado Keselj UW Math Grad Conference 2001 slide 5 Subgrammar Extraction Problem Given a grammar G and a set of words W  find a minimal grammar G 1 with the respect to a subgrammar relation  such that:  s  W * G(s) = G 1 (s) There can be no minimal grammars, or more than one.

6. Vlado Keselj UW Math Grad Conference 2001 slide 6 Subgrammar Extraction for CFGs Subgrammar definition: G 1  G 2 iff V 1  V 2,  1  2, P 1  P 2, S 1 =S 2 Context-Free Grammar: (V, , P, S) Recipe for CFGs: 1.  W 2. Apply the algorithm for removing useless symbols * ( O(n 3 ) time) * E.g., Aho Ullman 1979

7. Vlado Keselj UW Math Grad Conference 2001 slide 7 HPSG Grammars Hewrites. noun H: AGR: P: 3 N: sg G: m verb H: AGR: P: 3 N: sg P: 3 N: sg P: 3 N: sg 2 2 H: P: 3 N: sg G: m AGR: 1 1 1 sentence nounverb

8. Vlado Keselj UW Math Grad Conference 2001 slide 8 NP Completeness for HPSGs (p  q  r)  (  q  r   s)  (  p  q  s) 3-SAT problem: t1 ASGN: p: t (p  q  r) t1 ASGN: q: t (p  q  r) t1 ASGN: r: f (p  q  r) t2 ASGN: q: f (  q  r  s) t2 ASGN: r: t (  q  r  s) t2 ASGN: s: f (  q  r  s) start ASGN: 1 t1 ASGN: 1  t2 ASGN: 1  t3 ASGN: 1

9. Vlado Keselj UW Math Grad Conference 2001 slide 9 ASGN: t1 ASGN: q: t (p  q  r) t1 ASGN: r: f (p  q  r) t1 p: t (p  q  r) t2 ASGN: q: f (  q  r  s) t2 ASGN: r: t (  q  r  s) t2 ASGN: s: f (  q  r  s) NP Completeness for HPSG (continued) (p  q  r)  (  q  r   s)  (  p  q  s) satisfied for: p=true q=false s=true t1 ASGN: 1  p: t t1 ASGN: 1  p: t t1 ASGN: 1 p: t start ASGN: 1 p: t q: f s: t

10. Vlado Keselj UW Math Grad Conference 2001 slide 10 An Approximate Efficient Solution for HPSGs 1. remove all features from G and obtain G 1 E.g., a rule: is mapped to: typeX... typeY1... typeY2... typeXtypeY1typeY2... 2. apply subgrammar extraction to G 1 and obtain G 2 3. recover features in G 2 and obtain the solution G 3 Running time complexity: O(size(G). |Rule|)

11. Vlado Keselj UW Math Grad Conference 2001 slide 11 Overview • notion of subgrammar • notion of subgrammar extraction • efficient algorithm for CFGs • NP completeness for HPSGs • an approximate solution for HPSGs