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LING 581: Advanced Computational Linguistics

Explore quantifiers and set relations in computational linguistics, with examples and solutions for handling coordination in grammars. Learn how to express quantifiers using set relations between predicates.

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LING 581: Advanced Computational Linguistics

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  1. LING 581: Advanced Computational Linguistics Lecture Notes April 5th

  2. Today’s Topics • Homework Revisited • Part 3: Presentations • Proposal for FNA/Treatise corpora experiments

  3. Last Time: Montague-style • One possible solution:

  4. Last Time: Barwise-Cooper style • Possible solution (needs modification):

  5. Last Time: Barwise-Cooper style fails because it stops for each instantiation (reading) of _G312

  6. Last Time: Barwise-Cooper style • Use Var^ with setof or findall:

  7. Quantifiers: Homework Part 3: Coordination • Extend your two grammars to handle • Every man and every woman likes John

  8. Other Quantifiers • Other quantifiers can also be expressed using set relations between two predicates: Example: no: {X: P1(X)} ∩ {Y: P2(Y)} = ∅ ∩ = set intersection ∅ = empty set no man smokes {X: man(X)} ∩ {Y: smokes(Y)} = ∅ should evaluate to true for all possible worlds where there is no overlap between men and smokers men smokers

  9. Other Quantifiers • Other quantifiers can also be expressed using set relations between two predicates: Example: some: {X: P1(X)} ∩ {Y: P2(Y)} ≠∅ ∩ = set intersection ∅ = empty set some men smoke {X: man(X)} ∩ {Y: smokes(Y)} ≠ ∅ men smokers

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