# 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 . 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.

 Title Boolean-valued function Canonical name BooleanvaluedFunction Date of creation 2013-03-22 17:58:12 Last modified on 2013-03-22 17:58:12 Owner Jon Awbrey (15246) Last modified by Jon Awbrey (15246) Numerical id 10 Author Jon Awbrey (15246) Entry type Definition Classification msc 68Q01 Classification msc 68P01 Classification msc 06E30 Classification msc 03G05 Classification msc 03C55 Classification msc 03B05 Classification msc 68R01 Synonym characteristic function Synonym indicator function Synonym predicate Synonym proposition Related topic BooleanDomain Defines Boolean function