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.