1. November 2003CSA4050: Semantics I1 CSA4050: Advanced Topics in NLP Semantics I What is semantics for? Role of FOL Montague Approach

2. November 2003CSA4050: Semantics I2 Semantics Semantics is the study of the meaning of NL expressions Expressions include sentences, phrases, and sentences. What is the goal of such study? –Provide a workable definition of meaning. –Explain semantic relations between expressions.

3. November 2003CSA4050: Semantics I3 Workable Definition of Meaning Restrict the scope of semantics. Ignore irony, metaphor etc. Stick to the literal interpretations of expressions Assume that meaning is understood in terms of something concrete: truth conditions.

4. November 2003CSA4050: Semantics I4 Truth Conditional Semantics Key Claim: the meaning of a sentence is identical to the conditions under which it is true. Know the meaning of "Ġianni ate fish for tea" = know exactly how to apply it to the real world and decide whether it is true or false. On this view, one task of semantic theory is to provide a system for identifying the truth conditions of sentences.

5. November 2003CSA4050: Semantics I5 TCS and Semantic Relations TCS provides a precise account of semantic relations between sentences. Examples: –S1 is synonymous with S2. –S1 entails S2 –S1 is consistent with S2. –S1 is inconsistent with S2. Just like logic! Which logic?

6. November 2003CSA4050: Semantics I6 NL Semantics: Two Basic Issues How can we automate the process of associating semantic representations with expressions of natural language? How can we use semantic representations of NL expressions to automate the process of drawing inferences? We will focus mainly on first issue.

7. November 2003CSA4050: Semantics I7 Associating Semantic Representations Automatically Design a semantic representation language. Figure out how to compute the semantic representation of sentences Link this computation to the grammar and lexicon.

8. November 2003CSA4050: Semantics I8 Semantic Representation Language Logical form (LF) is the name used by logicians (Russell, Carnap etc) to talk about the representation of context- independent meaning. Semantic representation language has to encode the LF. One concrete representation for logical form is first order logic (FOL)

9. November 2003CSA4050: Semantics I9 Why is FOL a good thing? Has a precise, model-theoretic semantics. If we can translate a NL sentence S into a sentence of FOL, then we have a precise grasp on at least part of the meaning of S. Important inference problems have been studied for FOL. Computational solutions exist for some of them. Hence the strategy of translating into FOL also gives us a handle on inference.

10. November 2003CSA4050: Semantics I10 Anatomy of FOL Symbols of different types –constant symbols: a, b, c. –variable symbols: x, y, z –function symbols: f, g, h –predicate symbols: p, q, r –connectives: &, v,  –quantifiers: ,  –punctuation: ), (, “,”

11. November 2003CSA4050: Semantics I11 Anatomy of FOL Expressions of different types –Expressions for talking about things constant: a variable: x term: f(a,g(c,y)) –Expressions for stating facts atomic formula: p(a,x). complex formula: p(a,x) & q(y,b) Quantified expression:  x(p(a,x))

12. November 2003CSA4050: Semantics I12 wordPOSLogicRepresentation Mikeproper nounindividual constant mike cowcommon noun1 place predicate cow(x) redadjective1 place predicate red(x) big red caradj/noun1 place predicate big(x) & red(x) & car(x) sleepsintrans verb1 place predicate sleep (x) kickstrans. verb2 place predicate kick(x,,y) givesditrans verb3 place predgive(x,y,z) Logical Form of Phrases

13. November 2003CSA4050: Semantics I13 Logical Forms of Sentences John kicks Fido: kick(john, fido) Every student wrote a program  x( stud(x)   y( prog(y) & write(x,y))  y(  x(stud(x)  prog(y) & write(x,y)) Ambiguity problem Compositionality.

14. November 2003CSA4050: Semantics I14 Frege’s Principle of Compositionality The POC states that the LF of a complex phrase can be built out of the LFs of the constituent parts. An everyday example of compositionality is the way in which the “meaning” of arithmetic expressions is computed (2+3) * (4/2) = (5 * 2) = 10

15. November 2003CSA4050: Semantics I15 Compositionality for NL The LF of the whole sentence can be computed from the LF of the subphrases, i.e. Given the syntactic rule X  Y Z. Suppose [Y], [Z] are the LFs of Y, and Z respectively. Then [X] =  ([Y],[Z]) where  is some function for semantic combination

16. November 2003CSA4050: Semantics I16 Claims of Richard Montague: Each syntax rule is associated with a semantic rule that describes how the LF of the LHS category is composed from the LF of its subconstituents 1:1 correspondence between syntax and semantics (rule-to-rule hypothesis) Functional composition proposed for combining semantic forms. Lambda calculus proposed as the mechanism for describing functions for semantic combination.

17. November 2003CSA4050: Semantics I17 Sentence Rule Syntactic Rule: S  NP VP Semantic Rule: [S] = [VP]([NP]) i.e. the LF of S is obtained by "applying" the LF of VP to the LF of NP. For this to be possible [VP] must be a function, and [NP] the argument to the function.

18. November 2003CSA4050: Semantics I18 S write(bertrand,principia) NP bertand VP y.write(y,principia) V x. y.write(y,x) NP principia bertrand writes principia Parse Tree with Logical Forms