1. 0 Montague Grammar EECS 595 - Fall 2004 Amy Kao

2. 1 Montague Grammar Maps syntactic structure with semantic structure Uses formal language to describe natural language (1970) Universal Grammar Theory of formal syntax and semantics applied to formal & natural languages (1970) English as a formal language Theory of English as a form of formal language (1973) The Proper Treatment of Quantification in Ordinary English Application of Universal Grammar theories of a fragment of English

3. 2 Relevant Contributors Richard Montague (1930-1971) Student of Tarski Created Philosophies and Theories of Montague Grammar Taught at UCLA Barbara Hall Partee Student of Chomsky Wrote interpretations that made Montague’s work more understandable Teaches at U. Mass Amherst

4. 3 Syntactic Categories

5. 4 Category Definitions/Generation Categories are of form: X/Y – semantics of Y into the truth value of X Abbreviations for first 5 categories –IV = t/e –T = t/IV –TV = IV/T –IAV = IV/IV –CN = t//e Infinite number of possible categories –May use as many slashes as needed for new categories

6. 5 Example Expressions

7. 6 Example Rule F 3 For B TV F 3 ( ,  ) = If first word of  is a TV:   if  is not a variable  him i if  is he i If  is  1  2 where  1 is a TV/T:  1   2 if  is not a variable  him i  2 if  is he i F 3 (shave, a fish) = shave a fish F 3 (seek, he 1 ) = seek him 1 F 3 (read a large book, Mary) = read Mary a large book

8. 7 Syntactic Rules If   X/Y and   Y then F i ( ,  )  X Mary loves him, I, F 1 (love him, Mary) love him, IV, F 3 (love, he)Mary, T he, Tlove, TV

9. 8 Extensions and Intensions Extension: Semantic interpretation Intension: Function generating an extension Extension Problem

10. 9 Intensional Logic (IL) IL = Intensions and Types Syntactic Category Rule = Semantic Rule = Type ^X = intension of X –Example: if J = John, ^J = function returning individual named John If   X/Y and   Y and ,  translates into  ’  ’, then F i ( ,  ) translates into  ’(^  ’). Semantic Primitive t = truth values Semantic type is function of model view

11. 10 Truth Definitions

12. 11 Model Theoretic Semantics Semantics based on truth conditions –Tarski’s Model Theory (1954) IL is based on truth Conditions 3 Levels of Symbols –Logical Constants: =, , etc –Variables: As in traditional math –Non-logical Constants: , , relation symbols, function symbols, and constant individual symbols

13. 12 General Quantification & Compositionality Compositionality: phrase’s meaning derived from meaning of constituents & syntactic structure General Quantification: allows for syntax and semantic structure to be equivalent

14. 13 Controversies Formal Logic –Opposition: differing views of what semantics is Chomskyan: semantics is branch of psychology Semantists: semantics different from knowledge of semantics –Defense: Montague’s “English as a Formal Language” –Formal Semantics now mainstream Model Theory –Opposition: Prefer more concrete expressions –Defense: Understands sentences in terms of human mental models Truth Conditions –Opposition: Brings in too many irrelevant factors –Defense: Humans judge sentences based on context

15. 14 Developments Influenced by Montague Grammar Head-Driven Phrase Structure Grammar (HPSG) –Influenced by syntactic categories File Change Semantics(FCS) Discourse Representation Semantics (DRS) Situation Semantics Extended Categorical Grammar Generalized Phrase Structure Grammar (GPSG) Lexical Semantics