In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula , the symbol is a predicate which applies to the individual constant . Similarly, in the formula , is a predicate which applies to the individual constants and .

In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula would be true on an interpretation if the entities denoted by and stand in the relation denoted by . Since predicates are non-logical symbols, they can denote different relations depending on the interpretation used to interpret them. While first-order logic only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates.

Predicates in different systems

See also


  1. ^ Lavrov, Igor Andreevich; Maksimova, Larisa (2003). Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms. New York: Springer. p. 52. ISBN 0306477122.