Boolean-valued function

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

A Boolean function (of finite 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 (http://planetmath.org/Model). When necessary to avoid confusion, terms like propositional expression or predicate formula may be used to distinguish signs (http://planetmath.org/SignRelation) from their objects.