# Model (semantics)

**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.

### 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) V_{M}(p & q) = 1 if and only if V_{M}(p) = 1 and V_{M}(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) V_{M}( P(c) ) = 1 iff I_{M}(c) in I_{M}(P)

### Links

Utrecht Lexicon of Linguistics

### References

- Gamut, L.T.F. 1991.
*Logic, language, and meaning,*Univ. of Chicago Press, Chicago.