Predicate logic is a formal system for representing statements about objects, properties, and relationships using variables and quantifiers. It extends propositional logic and is widely used in mathematics, philosophy, linguistics, and knowledge representation.
(Also first-order logic, predicate logic, and first-order predicate calculus.) A collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects and allows the use of sentences that contain variables, so that rather than propositions such as Socrates is a man one can have expressions in the form "there exists x such that x is Socrates and x is a man" and there exists is a quantifier while x is a variable. in this sense, propositional logic is the foundation of first-order logic.