Ling 310 The Structure of Meaning, Lecture 6 B. H. Partee, March 8, 2006 NZ6MiniFragment.doc Page 1 3/4/2006 5:24 PM Lecture 6: A Mini-Fragment of English. What we Can and Can’t do with Just First-Order Logic. 1. English Mini-Fragment 1..........................................................................................................................................1 1.0 Introduction ........................................................................................................................................................1 1.1. Syntactic categories and their semantic types.....................................................................................................1 1.2. Syntactic Rules and Semantic Rules...................................................................................................................2 1.2.1. Basic syntactic rules ....................................................................................................................................3 1.2.2. Semantic interpretation of the basic rules. ..................................................................................................3 1.2.3. Syntax and semantics of Relative clauses, primitive version.......................................................................4 1.3. Lexicon...............................................................................................................................................................5 2. Examples ...................................................................................................................................................................6 3. Representations of meanings of English sentences in predicate logic vs. compositional interpretation of English syntax ...............................................................................................................................................................6 1. English Mini-Fragment 1. 1.0 Introduction In this handout we present a small and partial sample English grammar (a “fragment”, in MG terminology), that is, an explicit description of the syntax and semantics of a small part of English. A real fragment (of which this is just a “mini” or “preview” version) can serve several purposes: making certain aspects of formal semantics more explicit, including (and illustrating) more of the basics of the background logic. A reasonable-sized fragment is of interest in its own right in exploring the syntax and semantics of English. This mini-fragment, with its very minimal lexicon, mainly just puts together what we’ve seen so far, making some of it slightly more explicit. If we don’t get through it all today, we’ll continue with it in Lecture 6 next Wednesday. The semantics of the fragment will be given via translation into predicate logic supplemented with the iota-operator for definite descriptions. In later fragments in parts II and III we’ll have the added power of the lambda calculus and higher types. Here we’ll show in fine print some of the things we’re NOT including yet, including the kinds of adjectives that need to be interpreted as functions, and the treatment of quantified noun phrases in higher types. We’ll come back to those things later. Now we introduce the fragment of English: first the syntactic categories and the category-type correspondence, then the basic syntactic rules and the principles of semantic interpretation, and then a small lexicon and some meaning postulates. In Section 2 we present some examples. Certain rules of the fragment are postponed to Section 3 where they receive separate discussion; these are rules that go beyond the simple phrase structure rule schemata of Section 1. 1.1. Syntactic categories and their semantic types. Syntactic Semantic type Expressions category ============================================================== S t sentence ProperN e name (John)Ling 310 The Structure of Meaning, Lecture 6 B. H. Partee, March 8, 2006 NZ6MiniFragment.doc Page 2 3/4/2006 5:24 PM CN(P) e → t common noun (phrase) (cat) TCN(P) <e,e> → t relational common noun (phrase) (father) NP (i) e “e-type” or “referential” NP (John, the king) (ii) e → t predicative NP (a student, a king) ADJ(P) e → t intersective adjective (phrase) (carnivorous, happy) REL e → t relative clause (who(m) Mary loves) VP, IV e → t verb phrase, intransitive verb (loves Mary, is tall) TV <e,e> → t transitive verb (loves, sees) is none temporary treatment as in first-order logic: pretend it isn’t there! DET (i) function from type e→t to type e the (ii) function from type e→t to type e→t a (iii) function from type <e,e>→t to type e Mary’s 1.2. Syntactic Rules and Semantic Rules. Two different approaches to semantic interpretation of natural language syntax (both compositional, both formalized, and illustrated, by Montague): A. Direct Model-theoretic interpretation: Semantic values of natural language expressions (or their “underlying structure” counterparts) are given directly in model-theoretic terms; no intermediate language like Montague’s intensional logic (but for some linguists there is a syntactic level of “logical form” to which this model-theoretic interpretation applies, so the distinction between the two strategies is not always sharp.) This is the direct “English as a formal language” strategy. For illustration, see Heim and Kratzer (1998). Also see the discussion in Larson’s chapter 12. B. Interpretation via translation: Stage 1: compositional translation from natural language to a language of semantic representation, such as Montague’s intensional logic or, for now, into a slightly enriched version of first-order predicate logic. For an expression  of category C formed from expressions  of category A and  of category B, determine TR(γ) as a function of TR(α) and TR(β). Stage 2: Apply the compositional model-theoretic interpretation rules to the intermediate language. We will follow a mixture of the two strategies, using Predicate Logic slightly enriched as our logical language where we can, and giving model theoretic rules where predicate logic can’t express what we need to express.Ling 310 The Structure of Meaning, Lecture 6 B. H. Partee,