Model theory/Model Theoretic Semantics

Model theory was developed as a branch of mathematical logic as a method for studying the relationship between a formal language and its subject-matter. It provides rules for assigning semantics (truth-conditions) to artificial languages, such as predicate logic. An interpretation function is constructed for mapping the symbols and formulae of a language on to elements in the model (interpretation). The semantics of complex expressions in the language is then defined in terms of their parts.

The truth-conditional approach to meaning (see Frege; truth-conditions) allowed model theory to be extended to the study of natural languages. Sentences and their parts are mapped on to elements of a model, which represents the truth-conditions for the sentences. In possible world semantics, models are not restricted to domains of real entities but include possible objects; that is, model theory can provide truth-conditions in terms of possible worlds, thus allowing meaningful expressions without requiring ontological commitment. Model theory has also been applied to situation semantics, in which sentence-meanings are not given by truth-conditions but defined in terms of relations between situations, which include information about speakers as well as information about the world. (See compositionality; recursive rules)

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