Formal semantics (natural language)

Formal semantics studies the denotations of linguistic expressions. It is distinct from pragmatics, which encompasses aspects of meaning which arise from interaction and communicative intent. Particular high-level concerns include the nature of meaning, the nature of linguistic convention, and compositionality. Key topic areas include scope, modality, anaphora, tense, and aspect. However, semanticists vary in how they understand the metaphysical underpinnings of their work. Particularly within philosophy, formal semantics is viewed as a species of philosophy of language, the nature of broad concepts such as communication, convention and truth.[1] Others, particularly within linguistics, tend to view it as part of the study of linguistic cognition. As a result, philosophers put more of an emphasis on conceptual questions while linguists focus more on the syntax-semantics interface and crosslinguistic variation.[2][3]

Formal semantics emerged as a major area of research in the early 1970s, with the pioneering work of the philosopher and logician Richard Montague. Montague proposed a system now known as Montague grammar which consisted of a novel syntactic formalism for English, an intermediate language called IL, and a set of translation rules which linked the two. Montague grammar has been compared to a Rube Goldberg machine, but it was earth-shattering when first proposed and many of its insights survive in the semantic models which have superseded it.[4][5][6]

Montague's work was a major advance because it showed that natural languages could be treated like an interpreted formal language. Although modern formal semantics subsumes work by pre-Montague logicians, those logicians themselves tended to regard natural language as illogical. Similarly, the prevailing view within mid-20th century linguistics had been that language is too complex to allow for a treatment in terms of logic.[6] Montague's work was initially poorly received by some linguists including Noam Chomsky, leading Montague to tell Barbara Partee that she was "the only linguist who it is not the case that I can’t talk to".[6]

In subsequent work, Partee developed a new system which merged insights from Montague's work and transformational grammar. Subsequent work by Irene Heim, Angelika Kratzer, Tanya Reinhart, Robert May and others showed that Montague's key ideas could be more deeply worked into the generative framework by positing a level of syntactic representation called logical form which undergoes semantic interpretation.[6] Others such as Gerald Gazdar proposed models of the syntax-semantics interface which stayed closer in spirit to Montague's work, providing a system of interpretation in which denotations could be computed on the basis of surface structures. These approaches live on in frameworks such as categorial grammar.[7][6]

Most current approaches to formal semantics fall within the paradigm of the so-called truth-conditional semantics, which attempts to explain the meaning of a sentence by providing the conditions under which it would be true.[1][8] However, several adherents to the truth-conditional program have also argued that there is more to meaning than truth-conditions.[9] Alternative approaches include more cognitive-oriented proposals such as Pietroski's treatment of meanings as instructions to build concepts, sentences being devoid of truth-conditions.[10] Another line of inquiry, using linear logic, is glue semantics, which is based on the idea of "interpretation as deduction", closely related to the "parsing as deduction" paradigm of categorial grammar.[11]

Cognitive semantics emerged and developed as a reaction against formal semantics, but there have been recently several attempts at reconciling both positions.[12]