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# 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 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.

Defines:

Boolean function

Related:

BooleanDomain

Synonym:

characteristic function, indicator function, predicate, proposition

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

68Q01*no label found*68P01

*no label found*06E30

*no label found*03G05

*no label found*03C55

*no label found*03B05

*no label found*68R01

*no label found*

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