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1 Natural Language Processing Lecture 7 Unification Grammars Reading: James Allen NLU (Chapter 4)

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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

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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)

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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

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5 Sample Grammar (Abbreviated Form)

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6 Unification Grammars

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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:

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

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9 Graph Unification Algorithm

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10 Building new constituents using feature equations

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11 N1: (CAT N ROOT fish AGR {3s 3p}) ART1: (CAT ART ROOT the AGR {3s 3p}) NP ART N CAT 0 = NP CAT 1 = ART CAT 2 = N AGR = AGR 1 = AGR 2

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12 DAG Unification

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13 DAG Representation of happy

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14 The fish is happy

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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 CAT 0 =VP CAT 1 = V CAT 2 = {NP PP ADJP} ROOT 1 = be PRED 2 = +

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16 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)))

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17 Lexical Functional Grammars S NPVP ( SUBJ) = S NP VPSUBJ=1 0 = 2 aART( SPEC) = INDEF ( AGR = 3s) theART( SPEC) = DEF birdN( AGR = 3s) ( HEAD = BIRD)

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