logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...

, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula

P(a)

, the symbol

P

is a predicate which applies to the individual constant

a

. Similarly, in the formula

R(a,b)

R

is a predicate which applies to the individual constants

a

and

b

. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula

R(a,b)

would be true on an

interpretation Interpretation may refer to: Culture * Aesthetic interpretation, an explanation of the meaning of a work of art * Allegorical interpretation, an approach that assumes a text should not be interpreted literally * Dramatic Interpretation, an event ...

if the entities denoted by

a

and

b

stand in the relation denoted by

R

. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation used to interpret them. While

first-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quanti ...

only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates.

Predicates in different systems

* In propositional logic, atomic formulas are sometimes regarded as zero-place predicates In a sense, these are nullary (i.e. 0-

arity Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In ...

) predicates. * In