Semantics
Formal semantics

Formal semantics uses formal tools from logic and mathematics to analyze meaning in natural languages. It aims to develop precise logical formalisms to clarify the relation between expressions and their denotation. One of its key tasks is to provide frameworks of how language represents the world, for example, using ontological models to show how linguistic expressions map to the entities of that model. A common idea is that words refer to individual objects or groups of objects while sentences relate to events and states. Sentences are mapped to a truth value based on whether their description of the world is in correspondence with its ontological model.

Formal semantics further examines how to use formal mechanisms to represent linguistic phenomena such as quantification, intensionality, noun phrases, plurals, mass terms, tense, and modality. Montague semantics is an early and influential theory in formal semantics that provides a detailed analysis of how the English language can be represented using mathematical logic. It relies on higher-order logic, lambda calculus, and type theory to show how meaning is created through the combination of expressions belonging to different syntactic categories.

Dynamic semantics is a subfield of formal semantics that focuses on how information grows over time. According to it, "meaning is context change potential": the meaning of a sentence is not given by the information it contains but by the information change it brings about relative to a context.
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