Model is the device which makes it possible to interpret formal systems in model-theoretic semantics. The expressions of a formal language are then interpreted with respect to a model. In propositional logic, this model is an assignment of truth values to the basic propositional letters of the language.
the following example shows how complex expressions are interpreted in terms of the truth values that the model assigns to the propositional letters p and q.
(i) VM(p & q) = 1 if and only if VM(p) = 1 and VM(q) = 1
In predicate logic, the model M consists of a universe of discourse (D) and a mapping I from the individual constants and predicate letters to the universe of discourse. As the example shows, the interpretation of the formula P(c) is determined by the denotations that P and c get from the model.
(ii) VM( P(c) ) = 1 iff IM(c) in IM(P)
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.