Logical Forms Prof. Sameer Singh CS 295: STATISTICAL NLP WINTER - - PowerPoint PPT Presentation

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Logical Forms Prof. Sameer Singh CS 295: STATISTICAL NLP WINTER - - PowerPoint PPT Presentation

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Logical Forms Prof. Sameer Singh CS 295: STATISTICAL NLP WINTER 2017 February 16, 2017 Based on slides from Noah Smith, Dan Klein, Tom Kwiatkowski, and everyone else they copied from. Outline Logical Semantics Combinatory Categorical Grammar

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Logical Forms

  • Prof. Sameer Singh

CS 295: STATISTICAL NLP WINTER 2017

February 16, 2017

Based on slides from Noah Smith, Dan Klein, Tom Kwiatkowski, and everyone else they copied from.

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Outline

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Logical Semantics Combinatory Categorical Grammar

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Outline

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Logical Semantics Combinatory Categorical Grammar

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So far….

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Meaning of Words

  • Word Vectors
  • Parts of Speech
  • Named Entities
  • Word senses
  • ….

Meaning of Verbs

  • Context-free grammars
  • Thematic Roles
  • Semantic Roles
  • Dependency Relations
  • …

Still a gap between language and actionable representations

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Language “World”

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What is a good Korean restaurant near UCI campus? Meaning Representation

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A (Tiny) World Model

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Domain Amir, Brook, Chen, … Gogi Grill, Eureka, Cha Tea, UCI, … Korean, American, Beverages, .. Properties Amir, Brook, Chen, … are humans Gogi Grill is good, Cha Tea has a long wait, Eureka is noisy, They are restaurants.. Relations Gogi serves Korean, Eureka serves American, Cha Tea serves Beverages, Amir likes Gogi, Chen likes Korean, … a, b, c, … gg, er, ct, uci, .. ko, am, be, … Humans = {a, b, c, …} Good = {gg} Noisy={er} Restaurant={gg,er,ct} … Serves = {(gg,ko),(er,am), (ct,be), …} Likes={(a,gg),(c,ko),..} … Is Eureka noisy? Does Cha Tea serve beverages? What does Amir like? er in Noisy? (ct,be) in Serves? list (a,?) in Likes

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First-Order Logic

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Relations

  • Unary: Serves(x)
  • Binary: Likes(x,y)
  • n-ary: R(a1,..,an)

Terms

  • Constant: a,b,c,gg,ct
  • Variables: x,y,z

Formula

  • n-ary relation, R, and n terms (t1,..,tn),

then R(t1,..,tn) is a formula

  • If F is a formula, then so is ┐F
  • Boolean operators: F˅F, F˄F, F→F
  • Quantifiers:
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Translating b/w FoL and NL

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  • Gogi is not loud
  • Some humans like American
  • If a person likes Eureka, they aren’t friends with Brook
  • Every restaurant has a long wait or is disliked by Amir
  • Everybody has something they don’t like
  • There exists something that nobody likes
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Logical Semantics

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Montague, 1970

The denotation of a natural language sentence is the set of conditions that must hold in the (model) world for the sentence to be true. This is called the logical form of the sentence. Everybody has something they don’t like.

  • Less ambiguous
  • Can check truth value by querying a database
  • If you know it’s true, you can update database
  • Questions become queries on the database
  • Comprehending a document is same as chaining
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λ-Calculus

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Montague, 1970

Abstraction Application

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Example of λ-applications

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Montague, 1970

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Semantic Attachments to CFG

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Montague, 1970

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CFG to λ-Calculus

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CFG to λ-Calculus

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CFG to λ-Calculus

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CFG to λ-Calculus

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Tricky Cases: Transitive Verbs

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Steedman, 2000

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Tricky Cases: Indefinites

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Steedman, 2000

Bob ate a waffle. Amy ate a waffle.

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Tricky Cases: Tenses and Events

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Steedman, 2000

Alice danced. Alice had been dancing when Bob sneezed.

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Tricky Cases: Adverbs

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Steedman, 2000

Bob sings terribly.

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Outline

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Logical Semantics Combinatory Categorical Grammar

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Combinatory Categorical Grammar

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Steedman, 2000

Syntax λ-Calculus

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CCG Types

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Steedman, 2000

Instead of non-terminals, it has infinitely large set of categories or types Primitive Complex

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CCG Combinators

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Steedman, 2000

Instead of rules, we have a small set of generic combinators.

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Application Combinator

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Steedman, 2000

Forward Backward

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Conjunction Combinator

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Steedman, 2000

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Conjunction Combinator

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Steedman, 2000

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Composition Combinator

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Steedman, 2000

Forward Backward

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Type-Raising Combinator

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Steedman, 2000

Forward Backward

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Upcoming…

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  • Homework 3 is due on February 27
  • Write-up and data has been released.

Homework

  • Status report due in 2 weeks: March 2, 2017
  • Instructions coming soon
  • Only 5 pages

Project

  • Paper summaries: February 17, February 28, March 14
  • Only 1 page each

Summaries