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Unification Grammars

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

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Unification Grammars

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  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

  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 VP AGR0= AGR1 = AGR2 VFORM0 = VFORM2 NP  ART N AGR0 = AGR1 = AGR2

  5. Sample Grammar (Abbreviated Form)

  6. Unification Grammars

  7. Feature Structures as DAGs • Feature Structures are commonly represented as DAGs • Unification between FSs can be described as an operation that constructs a new DAG representing the unified structure • the Algorithm:

  8. Representing FSs as DAGs • Feature Structures: N1: (CAT N ROOT fish AGR {3s 3p}) N2: (CAT N AGR 3s) are represented as:

  9. Graph Unification Algorithm • To unify a DAG rooted at node Ni with a DAG rooted at node Nj: • 1. If Ni equals Nj, then return Ni and succeed. • 2. If both Ni and Nj are sink nodes, then if their labels have a non-null intersection, return a new node with the intersection as its label. Otherwise, the DAGs do not unify. • 3. If Ni and Nj are not sinks, then create a new node N. For each arc labeled F leaving Ni to node NFi, • 3a. If there is an arc labeled F leaving Nj to node NFj, then recursively unify NFi and NFj. Build an arc labeled F from N to the result of the recursive call. • 3b. If there is no arc labeled F from Nj, build an arc labeled F from N to NFi. • 3c. For each arc labeled F from Nj to node NFj, where there is no F arc leaving Ni, create a new arc labeled F from N to NFj.

  10. Building new constituents using feature equations

  11. N1: (CAT N ROOT fish AGR {3s 3p}) ART1: (CAT ART ROOT the AGR {3s 3p}) NP  ART N CAT0 = NP CAT1 = ART CAT2 = N AGR = AGR1 = AGR2

  12. DAG Unification

  13. DAG Representation of is happy

  14. The fish is happy

  15. 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 CAT0 =VP CAT1 = V CAT2 = {NP PP ADJP} ROOT1 = be PRED2 = +

  16. More Information in Lexicon put : (CAT V SUBCAT (FIRST (CAT NP) SECOND (CAT PP LOC +))) VP  V X2 X3 2 = FIRSTSUBCAT1 3=SECONDSUBCAT1 want : (CAT V SUBCAT (FIRST (CAT NP) SECOND (CAT VP VFORM inf)))

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