Formal semantics (natural language)

Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse engineering the semantic components of natural languages' grammars.
Overview.
Aims and scope.
Formal semantics studies the denotations of natural language expressions. High-level concerns include compositionality, nature of meaning, and reference. Key topic areas include scope, modality, anaphora, tense, and aspect. Semantics is distinct from pragmatics, which encompasses aspects of meaning which arise from interaction and communicative intent.
Formal semantics is an interdisciplinary field, often viewed as a subfield of both linguistics and philosophy, while also incorporating work from computer science, mathematical logic, and cognitive psychology. Depending on their particular background, formal semanticists may vary in how they view the nature of their enterprise. Particularly within philosophy, some formal semanticists adopt a Platonistic ontology and an externalist view of meaning. 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 issues while linguists are more likely to focus on the syntax-semantics interface and crosslinguistic variation.
History.
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 formal system now known as Montague grammar which consisted of a novel syntactic formalism for English, a logical system called Intensional logic, and a set of homomorphic 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when first proposed, and many of its fundamental insights survive in the various semantic models which have superseded it.
Montague Grammar was a major advance because it showed that natural languages could be treated as interpreted formal languages. Before Montague, many linguists had doubted that language could be understood in terms of logic, and logicians tended to view logic as a replacement for natural language rather than a tool for analyzing it. Montague's work was published during the Linguistics Wars, and was not initially well-received. It used then-niche formal tools, departed from then-standard assumptions about syntax, and its goals were at odds with those of linguists. While linguists wanted a restrictive framework which could only predict phenomena that occur in the grammars of actual human languages, Montague sought a more flexible framework which could characterize the concept of meaning in general. At one conference, Montague told Barbara Partee that she was "the only linguist who it is not the case that I can’t talk to".
In subsequent work, Partee developed a more linguistically plausible system which combined insights from both Montague Grammar 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. However, others such as Gerald Gazdar proposed models of the syntax-semantics interface which stayed closer to Montague's proposal, 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.
Varieties of formal semantics.
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. However, several adherents to the truth-conditional program have also argued that there is more to meaning than truth-conditions. 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. 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.
Cognitive semantics emerged and developed as a reaction against formal semantics, but there have been recently several attempts at reconciling both positions.