Editing Predicate (logic) (section)

== Predicates in different systems ==
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.
* In [[propositional logic]], [[atomic formula]]s are sometimes regarded as zero-place predicates.<ref name=lavrov>{{cite book|last1=Lavrov|first1=Igor Andreevich|first2=Larisa|last2=Maksimova|author2-link= Larisa Maksimova |title=Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms|year=2003|publisher=Springer|location=New York|isbn=0306477122|page=52|url=https://books.google.com/books?id=zPLjjjU1C9AC}}</ref> In a sense, these are nullary (i.e. 0-[[arity]]) predicates.
* In [[first-order logic]], a predicate forms an atomic formula when applied to an appropriate number of [[term (logic)|term]]s. 
* In [[set theory]] with the [[law of excluded middle]], predicates are understood to be [[Indicator function|characteristic functions]] or set [[indicator function]]s (i.e., [[function (mathematics)|functions]] from a set element to a [[truth value]]). [[Set-builder notation]] makes use of predicates to define sets.
* In [[autoepistemic logic]], which rejects the law of excluded middle, predicates may be true, false, or simply ''unknown''. In particular, a given collection of facts may be insufficient to determine the truth or falsehood of a predicate.
* In [[fuzzy logic]], the strict true/false valuation of the predicate is replaced by a quantity interpreted as the degree of truth.