Formal semantics (natural language)

Formal semantics is the scientific study of linguistic meaning through formal tools from logic and mathematics. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language.

Research in formal semantics aims to explain how speakers assign meanings to sentences they have never heard before. A key guiding methodological principle is the principle of compositionality, which states that the meaning of a complex expression depends on the meanings of its parts and the way they are combined. Semanticists typically formalize their hypotheses using the typed lambda calculus.

The meanings of sentences are often equated with the circumstances in which it would be true. These kinds of meanings can be modeled simply using Propositional and predicate logic. For complex phenomena, semanticists use more expressive tools such as possible world semantics, situation semantics, and dynamic semantics.

Using these and similar theoretical tools, formal semanticists investigate a wide range of linguistic phenomena crosslinguistically. They study quantificational expressions, which indicate the quantity of something, like the sentence "all ravens are black". An influential proposal analyzes them as relations between two sets—the set of ravens and the set of black things in this example. Quantifiers are also used to examine the meaning of definite and indefinite descriptions, which denote specific entities, like the expression "the president of Kenya". Formal semanticists are also interested in tense and aspect, which provide temporal information about events and circumstances. In addition to studying statements about what is true, semantics also investigates other sentences types such as questions and imperatives. Other investigated linguistic phenomena include intensionality, modality, negation, plural expressions, and the influence of contextual factors.

Formal semantics is relevant to various fields. In logic and computer science, formal semantics refers to the analysis of meaning in artificially constructed logical and programming languages. In cognitive science, some researchers rely on the insights of formal semantics to study the nature of the mind. Formal semantics has its roots in the development of modern logic starting in the late 19th century. Richard Montague's work in the late 1960s and early 1970s was pivotal in applying these logical principles to natural language, inspiring many scholars to refine his insights and apply them to diverse linguistic phenomena.