predicate calculus

The branch of symbolic logic that deals not only with relations between propositions as a whole but also with their internal structure, especially the relation between subject and predicate. Symbols are used to represent the subject and predicate of the proposition, and the existential or universal quantifier is used to denote whether the proposition is universal or particular in its application.

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The logical calculus in which the expressions include predicate letters, variables, and quantifiers, names, and operation letters, as well as the expressions for truth-functions and the propositional variables of the propositional calculus. The predicate calculus is the heart of modern logic, having proved capable of formalizing the central reasoning processes of modern mathematics and science. In a first-order predicate calculus the variables range over objects; in a higher-order calculus they may range over predicates and functions themselves. The first-order predicate calculus with identity includes ‘=’ as a primitive (undefined) expression: in a higher-order calculus it may be defined by the law that x = y iff (∀F)(Fx — Fy).

The noun has one meaning:

Meaning #1: a system of symbolic logic that represents individuals and predicates and quantification over individuals (as well as the relations between propositions)
  Synonym: functional calculus