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SEMANTICS: 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. EXAMPLE: 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)

LIT. Gamut, L.T.F. (1991)