Truth value

In logic, a truth value, or truth-value, is a value indicating to what extent a statement is true.

In classical logic, the only possible truth values are true and false. However, other values are possible in other logics. A simple intuitionistic logic has truth values of true, false, and unknown; fuzzy logic and other forms of multi-valued logic also use more truth values than simply true and false.

Algebraically, the set {true,false} forms a simple Boolean algebra. Other Boolean algebras may be used as sets of truth values in multi-valued logic, while intuitionistic logic generalises Boolean algebras to Heyting algebras.

In topos theory, the subobject classifier of a topos takes the place of the set of truth values.

This nomenclature is perhaps more consonant with usages that prevail in mathematics than with those of philosophy.