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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
predicate logic
predicate calculus
(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.
(2002-05-21)