A Boolean-valued function is a function of type , where is an arbitrary set and where is a Boolean domain.

A Boolean function (of finite arity ) is a Boolean-valued function of type .

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.