Formal semantics: what is it?

Formal semantics is an approach to semantics, the study of meaning, with roots in logic, the philosophy of language, and linguistics. The word formal in “formal semantics” is opposed to informal and reflects the influence of logic and mathematics in the rise of scientific approaches to philosophy and to linguistics in the twentieth century. Distinctive characteristics of this approach (see also Pagin, Chapter 3) have been truth conditions as a central part of meaning; (usually) a model-theoretic conception of semantics; and the methodological centrality of the Principle of Compositionality: “The meaning of a whole is a function of the meanings of its parts and their mode of syntactic combination.” Most formal semantics is model-theoretic, relating linguistic expressions to model-theoretically constructed semantic values cast in terms of truth, reference, and possible worlds or situations (hence, formal semantics is not “formal” in the sense of Hilbert, 1922). And most formal semanticists treat meaning as mind-independent (and abstract), not as concepts “in the head”; formal semanticists distinguish semantics from knowledge of semantics (Lewis, 1975b; Cresswell, 1978). This sets formal semantics apart from approaches which view semantics as relating a sentence principally to a representation on another linguistic “level” (logical form) (May, 1985) or a representation in an innate “language of thought” (Fodor, 1975) or “conceptual representation” (Jackendoff, 1992). 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 representation-language is (Lewis, 1970). Kamp's Discourse Representation Theory is an exception, since as noted in Section 1.3.3 below, it includes as essential an intermediate level of representation with claimed psychological reality. Formal semantics is centrally concerned with compositionality at the syntax–semantics interface (see Sailer, Chapter 21), how the meanings of larger constituents are built up from the meanings of their parts on the basis of their syntactic structure.

The most important figure in the history of formal semantics was undoubtedly Richard Montague (1930–1971), whose seminal works in this area date from the late 1960s and the beginning of the 1970s. Other important contributors will also be discussed below. Since the 1980s formal semantics has been a core area of linguistic theory; important contributions also continue to come from philosophy, logic, cognitive science, and computational linguistics.