Talk:PlanetPhysics/Boolean Valued Function

Original TeX Content from PlanetPhysics Archive

%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: boolean-valued function %%% Primary Category Code: 02. %%% Filename: BooleanValuedFunction.tex %%% Version: 2 %%% Owner: Jon Awbrey %%% Author(s): Jon Awbrey %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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A \textbf{boolean-valued function} is a \htmladdnormallink{function}{http://planetphysics.us/encyclopedia/Bijective.html} of \htmladdnormallink{type}{http://planetphysics.us/encyclopedia/Bijective.html} $f : X \to \mathbb{B}$, where $X$ is an arbitrary set and where $\mathbb{B}$ is a \htmladdnormallink{boolean domain}{http://planetphysics.us/encyclopedia/BooleanDomain.html}.

A \textbf{boolean function} (of finite \htmladdnormallink{arity}{http://planetphysics.us/encyclopedia/Bijective.html} $k$) 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 models. When necessary to avoid confusion, terms like \textit{propositional expression} or \textit{predicate formula} may be used to distinguish signs from their objects.

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