PlanetPhysics/Boolean Valued Function

A boolean-valued function is a [[../Bijective/|function]] of [[../Bijective/|type]] $f:X\to 𝔹$, where $X$ is an arbitrary set and where $𝔹$ is a [[../BooleanDomain/|boolean domain]].

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

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.