Boolean-valued function

A Boolean-valued function is a function of type $f:X\to 𝔹$, 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 $f:{𝔹}^k\to 𝔹$.

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 (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