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A predicate is a logical expression that evaluates to either true or false. In set theory, predicates are used to define sets; a set contains all of the elements from some greater set for which the predicate is true.
The NSPredicate class was added to Cocoa at the same time as Spotlight. It is used when searching metadata in the Spotlight database, but can also be used in a variety of other places. Each NSPredicate instance represents a single predicate expression.