1 Unification Grammars Allen ’ s Chapter 4 J&M ’ s Chapter 11

2 Unification of Feature Structures Key concept - extension relationship between two FSs: F2 extends F1 if every feature-value pair in F1 is also in F2 Two FSs F1 and F2 unify if there exists a FS F that is an extension of both of them The Most General Unifier is the minimal FS F that extends both The Unification operation allows easy expression of grammatical relationships among constituent feature structures

3 Unification of Feature Structures F2 extends F1: F1 = (CAT v) F2 = (CAT v ROOT cry) F1 = (AGR {3s 3p}) F2 = (AGR 3s) F3 is MGU of F1 and F2: F1 = (CAT v ROOT cry), F2 = (CAT v VFORM pres), F3 = (CAT v ROOT cry VFORM pres) F1 and F2 do not unify: F1 = (CAT v AGR 3s) F2 = (CAT v AGR 3p)

4 Unification-based Grammars Grammar rules can be completely specified using unification Example: X0 --> X1 X2 CAT X0 = S CAT X1 = NP CAT X2 = VP AGR0 =AGR1 = AGR2 VFORM0 = VFORM2 If a feature (such as CAT) is always specified, it can be associated with the non-terminal of a CFG rule Examples: S  NP VPAGR0= AGR1 = AGR2 VFORM0 = VFORM2 NP  ART N AGR0 = AGR1 = AGR2

5 Sample Grammar (Abbreviated Form)

6 Unification Grammars

7 Predicative Phrases VP  (V ROOT be) (NP PRED +) He is a student VP  (V ROOT be) (PP PRED +) He is in the house VP  (V ROOT be) (ADJP PRED +) He is happy X0  X1 X2 CAT 0 =VP CAT 1 = V CAT 2 = {NP PP ADJP} ROOT 1 = be PRED 2 = +

8 More Information in Lexicon put : (CAT V SUBCAT (FIRST (CAT NP) SECOND (CAT PP LOC +))) VP  V X 2 X 3 2 = FIRST SUBCAT1 3=SECOND SUBCAT1 want : (CAT V SUBCAT (FIRST (CAT NP) SECOND (CAT VP VFORM inf)))