model-theoretic semantics

A version of TRUTH-CONDITIONAL SEMANTICS developed by Richard Montague (1930–71) and others. A class of MODELS is defined for each LANGUAGE, and RULES are formulated assigning TRUTH VALUES to SENTENCES relative to each model. Such notions as LOGICAL CONSEQUENCE and LOGICAL TRUTH may then be defined by quantifying over the models relative to which given sentences are true. Typically, a model consists of three components: (a) a set of individuals, taken to constitute the domain of DISCOURSE; (b) an arbitrary number of world–time pairs; and (c) an assignment of an EXTENSION for each LEXICAL item relative to each world–time pair.