Editing Formal language (section)

====Interpretations and models====
{{main|Formal semantics (logic)||Interpretation (logic)|Model theory}}

Formal languages are entirely syntactic in nature, but may be given [[semantics]] that give meaning to the elements of the language. For instance, in mathematical [[logic]], the set of possible formulas of a particular logic is a formal language, and an [[interpretation (logic)|interpretation]] assigns a meaning to each of the formulas—usually, a [[truth value]].

The study of interpretations of formal languages is called [[Formal semantics (logic)|formal semantics]]. In mathematical logic, this is often done in terms of [[model theory]]. In model theory, the terms that occur in a formula are interpreted as objects within [[Structure (mathematical logic)|mathematical structures]], and fixed compositional interpretation rules determine how the truth value of the formula can be derived from the interpretation of its terms; a ''model'' for a formula is an interpretation of terms such that the formula becomes true.