[Logic] A predicate or relation is a function that maps its arguments to the truth values 1 and 0 or T and F. (Knowledge Representation, John F. Sowa, 2000, Brooks Cole, pg. 468).
[Logic] Predicate is short for ... Propositional Function P(x1,x2,...,xn), for n >= 0 if (independent) variables. (Mathematical Logic, Stephen Kleene,1967, John Wiley & Sons, pg. 74).
[Informally] A predicate is a statement that may be true or false depending on the values of its variables. It can be thought of as an operator or function that returns a value that is either true or false. For example, predicates are sometimes used to indicate set membership: when talking about sets, it is sometimes inconvenient or impossible to describe a set by listing all of its elements. Thus, a predicate P(x) will be true or false, depending on whether x belongs to a set.
Predicates are also commonly used to talk about the properties of objects, by defining the set of all objects that have some property in common.
- In some contexts a unary predicate is referred to as a property.