Logical Forms. Prof. Sameer Singh CS 295: STATISTICAL NLP WINTER February 16, 2017

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1 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.

2 Outline Logical Semantics Combinatory Categorical Grammar CS 295: STATISTICAL NLP (WINTER 2017) 2

3 Outline Logical Semantics Combinatory Categorical Grammar CS 295: STATISTICAL NLP (WINTER 2017) 3

4 So far. Meaning of Words Meaning of Verbs Word Vectors Parts of Speech Named Entities Word senses. Context-free grammars Thematic Roles Semantic Roles Dependency Relations Still a gap between language and actionable representations CS 295: STATISTICAL NLP (WINTER 2017) 4

5 Language World What is a good Korean restaurant near UCI campus? Meaning Representation CS 295: STATISTICAL NLP (WINTER 2017) 5

6 A (Tiny) World Model Domain Properties Relations Amir, Brook, Chen, Gogi Grill, Eureka, Cha Tea, UCI, Korean, American, Beverages,.. Amir, Brook, Chen, are humans Gogi Grill is good, Cha Tea has a long wait, Eureka is noisy, They are restaurants.. 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 CS 295: STATISTICAL NLP (WINTER 2017) 6

7 First-Order Logic Terms Constant: a,b,c,gg,ct Variables: x,y,z Relations Unary: Serves(x) Binary: Likes(x,y) n-ary: R(a 1,..,a n ) Formula n-ary relation, R, and n terms (t 1,..,t n ), then R(t 1,..,t n ) is a formula If F is a formula, then so is F Boolean operators: F F, F F, F F Quantifiers: CS 295: STATISTICAL NLP (WINTER 2017) 7

8 Translating b/w FoL and NL 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 CS 295: STATISTICAL NLP (WINTER 2017) 8

9 Logical Semantics Everybody has something they don t like. 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. 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 Montague, 1970 CS 295: STATISTICAL NLP (WINTER 2017) 9

10 λ-calculus Abstraction Application Montague, 1970 CS 295: STATISTICAL NLP (WINTER 2017) 10

11 Example of λ-applications Montague, 1970 CS 295: STATISTICAL NLP (WINTER 2017) 11

12 Semantic Attachments to CFG Montague, 1970 CS 295: STATISTICAL NLP (WINTER 2017) 12

13 CFG to λ-calculus CS 295: STATISTICAL NLP (WINTER 2017) 13

14 CFG to λ-calculus CS 295: STATISTICAL NLP (WINTER 2017) 14

15 CFG to λ-calculus CS 295: STATISTICAL NLP (WINTER 2017) 15

16 CFG to λ-calculus CS 295: STATISTICAL NLP (WINTER 2017) 16

17 Tricky Cases: Transitive Verbs Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 17

18 Tricky Cases: Indefinites Bob ate a waffle. Amy ate a waffle. Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 18

19 Tricky Cases: Tenses and Events Alice danced. Alice had been dancing when Bob sneezed. Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 19

20 Tricky Cases: Adverbs Bob sings terribly. Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 20

21 Outline Logical Semantics Combinatory Categorical Grammar CS 295: STATISTICAL NLP (WINTER 2017) 21

22 Combinatory Categorical Grammar Syntax λ-calculus Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 22

23 CCG Types Instead of non-terminals, it has infinitely large set of categories or types Primitive Complex Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 23

24 CCG Combinators Instead of rules, we have a small set of generic combinators. Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 24

25 Application Combinator Forward Backward Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 25

26 Conjunction Combinator Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 26

27 Conjunction Combinator Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 27

28 Composition Combinator Forward Backward Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 28

29 Type-Raising Combinator Forward Backward Steedman, 2000 CS 295: STATISTICAL NLP (WINTER 2017) 29

30 Upcoming Homework Homework 3 is due on February 27 Write-up and data has been released. Project Status report due in 2 weeks: March 2, 2017 Instructions coming soon Only 5 pages Summaries Paper summaries: February 17, February 28, March 14 Only 1 page each CS 295: STATISTICAL NLP (WINTER 2017) 30