A boolean-valued function is a function of type f : X → 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 : 𝔹k → 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.
