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A boolean-valued function, in some usages a predicate or a proposition, is a function of the type ${\displaystyle f:X\to \mathbb {B} }$, where ${\displaystyle X}$ is an arbitrary set, where ${\displaystyle \mathbb {B} }$ is a generic 2-element set, typically ${\displaystyle \mathbb {B} =\left\{0,1\right\}}$, and where the latter is frequently interpreted for logical applications as ${\displaystyle \mathbb {B} =\left\{false,true\right\}}$.

In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a boolean-valued 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.

Actually, boolean valued functions are stupid.