(Or "predicate calculus") An extension of propositional logic with separate symbols for predicates, subjects, and quantifiers.
For example, where propositional logic might assign a single symbol P to the proposition "All men are mortal", predicate logic can define the predicate M(x) which asserts that the subject, x, is mortal and bind x with the universal quantifier ("For all"):
All x . M(x)
Higher-order predicate logic allows predicates to be the subjects of other predicates.