Predicate (logic)

<h2 id="predicates-in-different-systems">Predicates in different systems</h2>
<p>A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values.
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<ul><li>In <a href="/facts/Propositional_logic/MNt5v31V">propositional logic</a>, <a href="/facts/Atomic_formula/s9WMnbqT">atomic formulas</a> are sometimes regarded as zero-place predicates.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> In a sense, these are nullary (i.e. 0-<a href="/facts/Arity/zSVuwHvP">arity</a>) predicates.</li>
<li>In <a href="/facts/First-order_logic/lcISqWIg">first-order logic</a>, a predicate forms an atomic formula when applied to an appropriate number of <a href="/facts/Term_(logic)/M0nXp7dH">terms</a>.</li>
<li>In <a href="/facts/Set_theory/1ptfsvUP">set theory</a> with the <a href="/facts/Law_of_excluded_middle/tDhbugCN">law of excluded middle</a>, predicates are understood to be <a href="/facts/Indicator_function/QEuh04NM">characteristic functions</a> or set <a href="/facts/Indicator_function/QEuh04NM">indicator functions</a> (i.e., <a href="/facts/Function_(mathematics)/CdReEKCh">functions</a> from a set element to a <a href="/facts/Truth_value/SY4e2w8l">truth value</a>). <a href="/facts/Set-builder_notation/0nVHQF6E">Set-builder notation</a> makes use of predicates to define sets.</li>
<li>In <a href="/facts/Autoepistemic_logic/2VoDItYh">autoepistemic logic</a>, which rejects the law of excluded middle, predicates may be true, false, or simply <i>unknown</i>. In particular, a given collection of facts may be insufficient to determine the truth or falsehood of a predicate.</li>
<li>In <a href="/facts/Fuzzy_logic/1PvN4Att">fuzzy logic</a>, the strict true/false valuation of the predicate is replaced by a quantity interpreted as the degree of truth.</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Classifying_topos/PyjMgsyW">Classifying topos</a></li>
<li><a href="/facts/Free_variables_and_bound_variables/ndWnXXYs">Free variables and bound variables</a></li>
<li><a href="/facts/Multigrade_predicate/6vra1GU6">Multigrade predicate</a></li>
<li><a href="/facts/Opaque_predicate/jcgM7B48">Opaque predicate</a></li>
<li><a href="/facts/Predicate_functor_logic/5yIqUrHA">Predicate functor logic</a></li>
<li><a href="/facts/Predicate_variable/vdoPP5Yu">Predicate variable</a></li>
<li><a href="/facts/Truthbearer/DN4IcCGv">Truthbearer</a></li>
<li><a href="/facts/Truth_value/SY4e2w8l">Truth value</a></li>
<li><a href="/facts/Well-formed_formula/YpTVlzuj">Well-formed formula</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://cs.odu.edu/~toida/nerzic/content/logic/pred_logic/predicate/pred_intro.html">Introduction to predicates</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Lavrov, Igor Andreevich; Maksimova, Larisa (2003). Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms. New York: Springer. p. 52. ISBN 0306477122. <a href="0306477122" target="_blank">0306477122</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Predicate (logic) open-in-new

Predicate (logic)