A boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true.

In mathematics and logic, a (finitary) Boolean function (or switching function) is a function of the form ƒ : B^k → B, where B = {0, 1} is a Boolean domain and k is a non-negative integer called the arity of the function. In the case where k = 0, the "function" is essentially a constant element of B.