UMass Amherst LINGUIST 310 - Lecture 1: Introduction to Formal Semantics and Compositionality

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Ling 310 The Structure of Meaning, Lecture 1 B.H. Partee, February 20, 2006 p.1 NZ1.doc Page 1 Lecture 1: Introduction to Formal Semantics and Compositionality 1. Compositional Semantics ................................................................................................................................... 1 1.1. The Principle of Compositionality.............................................................................................................. 1 1.2. Model-theoretic Semantics. ........................................................................................................................ 2 2. Linguistic Examples. ..........................................................................................................................................3 2.1. The structure of NPs with restrictive relative clauses. ................................................................................ 3 2.2. Phrasal and sentential conjunction..............................................................................................................4 REFERENCES. ...................................................................................................................................................... 4 “HOMEWORK” No. 0: Participant Questionnaire ............................................................................................. 5 Read for next time: (1) R. Larson (1995) Semantics. Chapter 12 in L. Gleitman and M.Liberman, eds. An Invitation to Cognitive Science, Vol I: Language. (D. Osherson, general editor), pp 361-380. (2) Partee, Barbara H. 1999. "Semantics" in R.A. Wilson and F.C. Keil, eds., The MIT Encyclopedia of the Cognitive Sciences. Cambridge, MA: The MIT Press. 739-742. Bring next time: Participant Questionnaire: see last page. 1. Compositional Semantics 1.1. The Principle of Compositionality. A basic starting point of generative grammar: there are infinitely many sentences in any natural language, and the brain is finite, so linguistic competence must involve some finitely describable means for specifying an infinite class of sentences. That is a central task of syntax. Semantics: A speaker of a language knows the meanings of those infinitely many sentences, is able to understand a sentence he/she has never heard before or to express a meaning he/she has never expressed before. So for semantics also there must be a finite way to specify the meanings of the infinite set of sentences of any natural language. A central principle of formal semantics is that the relation between syntax and semantics is compositional. The Principle of Compositionality: The meaning of an expression is a function of the meanings of its parts and of the way they are syntactically combined. Each of the key terms in the principle of compositionality is a “theory-dependent” term, and there are as many different versions of the principle as there are ways of specifying those terms. (meaning, function, parts (syntax) ) Some of the different kinds of things meanings could be in a compositional framework: (a) (early Katz and Fodor) Representations in terms of semantic features. bachelor: [+HUMAN, +MALE, +ADULT, +NEVER-MARRIED (?!)]. Semantic composition: adding feature sets together. Problems: insufficient structure for the representations of transitive verbs, quantifiers, and many other expressions; unclear status of uninterpreted features. (b) Representations in a “language of thought” or “conceptual representation” (Jackendoff, Jerry Fodor); if semantics is treated in terms of representations, then semantic composition becomes a matter of compositional translation from a syntactic representation to a semantic representation. (c) The logic tradition: Frege, Tarski, Carnap, Montague. The basic meaning of a sentence is its truth-conditions: to know the meaning of a sentence is to know what the world must be like if the sentence is true. Knowing the meaning of a sentence does not require knowingLing 310 The Structure of Meaning, Lecture 1 B.H. Partee, February 20, 2006 p.2 NZ1.doc Page 2 whether the sentence is in fact true; it only requires being able to discriminate between situations in which the sentence is true and situations in which the sentence is false. Starting from the idea that the meaning of a sentence consists of its truth-conditions, meanings of other kinds of expressions are analyzed in terms of their contribution to the truth-conditions of the sentences in which they occur. 1.2. Model-theoretic Semantics. In formal semantics, truth-conditions are expressed in terms of truth relative to various parameters — a formula may be true at a given time, in a given possible world, relative to a certain context that fixes speaker, addressee, etc., and relative to a certain assignment of meanings to its atomic “lexical” expressions and of particular values to its variables. For simple formal languages, all of the relevant variation except for assignment of values to variables is incorporated in the notion of truth relative to a model. Semantics which is based on truth-conditions is called model-theoretic. Compositionality in the Montague Grammar tradition: The task of a semantics for language L is to provide truth conditions for every well-formed sentence of L, and to do so in a compositional way. This task requires providing appropriate model-theoretic interpretations for the parts of the sentence, including the lexical items. The task of a syntax for language L is (a) to specify the set of well-formed expressions of L (of every category, not only sentences), and (b) to do so in a way which supports a compositional semantics. The syntactic part-whole structure must provide a basis for semantic rules that specify the meaning of a whole as a function of the meanings of its parts. Basic structure in classic Montague grammar: (1) Syntactic categories and semantic “types”: For each syntactic category there must be a uniform semantic type. For example, one could hypothesize that sentences express propositions, nouns and adjectives express properties of entities, verbs express properties of events. (2) Basic (lexical) expressions and their interpretation. Some syntactic categories include basic expressions; for each such expression, the semantics must assign an interpretation of the appropriate type. Within the tradition of formal semantics, most lexical


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UMass Amherst LINGUIST 310 - Lecture 1: Introduction to Formal Semantics and Compositionality

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