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 ).
Philosophy dictionary. Academic. 2011.