Formal semantics is an approach to SEMANTICS1, the study of meaning, with roots in logic, the philosophy of language, and linguistics, and since the 1980’s a core area of linguistic theory. Characteristics of formal semantics to be treated in this article include the following: Formal semanticists treat meaning as mind-independent (though abstract), contrasting with the view of meanings as concepts “in the head” (see I-LANGUAGE AND E-LANGUAGE and MEANING EXTERNALISM AND INTERNALISM); formal semanticists distinguish semantics from knowledge of semantics (Lewis (...) 1975, Cresswell 1978), which has consequences for the notion of semantic COMPETENCE. A central part of the meaning of a sentence on this approach is its TRUTH CONDITIONS, and most although not all formal semantics is model-theoretic, relating linguistic expressions to model-theoretically constructed semantic values cast in terms of truth, REFERENCE, and possible worlds. This sets formal semantics apart from approaches which view semantics as relating a sentence just to a representation on another linguistic “level” (LOGICAL FORM) or a representation in an innate LANGUAGE OF THOUGHT. The formal semanticist could accept such representations as an aspect of semantics but would insist on asking what the model-theoretic semantic interpretation of the given representationlanguage is (Lewis 1970). Formal semantics is centrally concerned with COMPOSITIONALITY at the SYNTAX-SEMANTICS INTERFACE, how the meanings of larger constituents are built up from the meanings of their parts on the basis of their syntactic structure, and with the relation between compositional SENTENCE MEANING and meaning in discourse. (shrink)

We started from the fact that type theory, in the way it was implemented in IL, makes it costly to deal with nominalization processes. We have also argued that the type hierarchy as such doesn't play any real role in a grammar; the classification it provides for different semantic objects is already contained, in some sense, in the categorial structure of the grammar itself. So, on the basis of a theory of properties (Cocchiarella's HST*) we have tried to build a (...) language (IL*) whose syntax does not contain any explicit typing of expressions. Some of the consequences that this move brings about in the overall organization of the grammar can be summarized as follows:it allows for a simple treatment of infinitives, gerunds, factives and, in general, all those phenomena which might be analyzed as cases of nominalization;it provides a simpler and more constrained semantics than IL, since IL* doesn't go beyond second order, and its non-modal basis is axiomatizable;it suggests that the role of logical form in a theory of grammar could be that of a family of theories of semantic objects;it eliminates the extrinsic limitations of a type hierarchy on the choice of the system of syntactic categories.I think that it is interesting to notice how having an explicit semantic framework helps to provide a sense in which it is legitimate to regard the syntax of a language as ‘autonomous’. (shrink)

In the spring of 1978, one of the authors of this book was sitting in on a course in logic for linguists given by the other author. In attempting to present some of Montague's insights in an elementary way, the authors began dis cussions aimed towards the construction of a simple model-theoretical semantic apparatus which could be applied directly to a small English-like language and used to illustrate the methods of formal logical interpretation. In these discussions two points impressed themselves (...) on us. First, our task could be simplified by using boolean algebras and boolean homomorphisms in the models; and second, the boolean approach we were developing had much more widespread relevance to the logical structure of English than we first thought. During the summer and fall of 1978 we continued work on the system, proving the more fundamental theorems and outlining the way in which an intensional interpretation scheme could be developed which made use of the boolean approach. We presented our findings in a monograph which the UCLA Linguistics Department kindly published as part of their series called Occa sional Papers in Linguistics; one of the authors also presented the system at a colloquium held at the Winter Meeting of the Linguistic Society of America in December 1978. (shrink)

This paper argues for the hypothesis of direct compositionality (as in, e.g., Montague 1974), according to which the combinatory syntactic rules specify a set of well-formed expressions while the semantic combinatory rules work in tandem to directly supply a model-theoretic interpretation to each expression as it is "built" in the syntax. (This thus obviates the need for any level like LF and, concomitantly, for any rules mapping surface structures to such a level.) I focus here on one related group of (...) phenomena: the interaction of "paycheck" pronouns with Weak Crossover effects and i-within-i effects. These interactions were studied in Jacobson (1977) as they show up in Back-Peters sentences. There I argued that these interactions show that paycheck pronouns have a complex representation at LF; here I show that all of the observations in this earlier work are compatible with the hypothesis of direct compositionality. The key tool is the adoption of a variation-free semantics (a semantics which makes no use of variables as part of the semantic machinery). In addition to the general consequences for the syntax/semantics interface, there are two other main results. First, I provide new arguments for a variable-free semantics. For example, it will be shown that under this view the paycheck reading of a pronoun comes for free; most other theories posit additional mechanisms and/or an additional lexical meaning for pronouns, and thus paycheck and regular pronouns are only accidentally homophonous. Second, I reiterate one of the central points in Jacobson (1977): this is that the first pronoun in a Bach-Peters sentence is indeed a paycheck pronoun, and hence nothing special needs to be said about these sentences nor does any new machinery need to be invoked for them. (shrink)

Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain difficulties with respect (...) to model theory and/or proof theory, difficulties which the current proposals are intended to resolve.Lambek calculus is complete for interpretation byresiduation with respect to the adjunction operation of groupoid algebras (Buszkowski 1986). In Moortgat and Morrill (1991) it is shown how to give calculi for families of categorial operators, each defined by residuation with respect to an operation of prosodic adjunction (associative, non-associative, or with interactive axioms). The present paper treats discontinuity in this way, by residuation with respect to three adjunctions: + (associative), (.,.) (split-point marking), andW (wrapping) related by the equations 1+s 2+s 3=(s 1,s 3)Ws 2. We show how the resulting methods apply to discontinuous functors, quantifier scope and quantifier scope ambiguity, pied piping, and subject and object antecedent reflexivisation. (shrink)