PlanetPhysics/Boolean Valued Function

A boolean-valued function is a function of type $f:X\to \mathbb {B}$, where $X$ is an arbitrary set and where $\mathbb {B}$ is a boolean domain.

A boolean function (of finite arity $k$) is a boolean-valued function of type $f:\mathbb {B} ^{k}\to \mathbb {B}$.

In some contexts a boolean-valued function may be referred to as a predicate or a proposition . In other contexts these terms may be used to describe the syntactic entities that denote or express boolean-valued functions, or that have boolean-valued functions among their canonical or intended models. When necessary to avoid confusion, terms like propositional expression or predicate formula may be used to distinguish signs from their objects.