A booleanvalued function, in some usages is a predicate or a proposition, is a function of the type f : X → B, where X is an arbitrary set and where B is a boolean domain.
A boolean domain B is a generic 2element set, say, B = {0, 1}, whose elements are interpreted as logical values, for example, 0 = false and 1 = true.
In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a booleanvalued function may also be referred to as a characteristic function, indicator function, predicate, or proposition. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding semiotic sign or syntactic expression.
In formal semantic theories of truth, a truth predicate is a predicate on the sentences of a formal language, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value.
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