68Q01-BooleanvaluedFunction.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{BooleanvaluedFunction}
\pmcreated{2013-03-22 17:58:12}
\pmmodified{2013-03-22 17:58:12}
\pmowner{Jon Awbrey}{15246}
\pmmodifier{Jon Awbrey}{15246}
\pmtitle{Boolean-valued function}
\pmrecord{10}{40476}
\pmprivacy{1}
\pmauthor{Jon Awbrey}{15246}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{68Q01}
\pmclassification{msc}{68P01}
\pmclassification{msc}{06E30}
\pmclassification{msc}{03G05}
\pmclassification{msc}{03C55}
\pmclassification{msc}{03B05}
\pmclassification{msc}{68R01}
\pmsynonym{characteristic function}{BooleanvaluedFunction}
\pmsynonym{indicator function}{BooleanvaluedFunction}
\pmsynonym{predicate}{BooleanvaluedFunction}
\pmsynonym{proposition}{BooleanvaluedFunction}
\pmrelated{BooleanDomain}
\pmdefines{Boolean function}

\endmetadata

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A \textbf{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 \textbf{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 \textit{predicate} or a \textit{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 \PMlinkname{models}{Model}.  When necessary to avoid confusion, terms like \textit{propositional expression} or \textit{predicate formula} may be used to distinguish \PMlinkname{signs}{SignRelation} from their objects.

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