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In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P {\displaystyle P} , the symbol P {\displaystyle P} is a predicate which applies to the individual constant a {\displaystyle a} . Similarly, in the formula R {\displaystyle R} , R {\displaystyle R} is a predicate which applies to the individual constants a {\displaystyle a} and b {\displaystyle b} .
In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R {\displaystyle R} would be true on an interpretation if the entities denoted by a {\displaystyle a} and b {\displaystyle b} stand in the relation denoted by R {\displaystyle R} . 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.