First-order logic

First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is 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", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.

First-order logic - Wikipedia Jump to content From Wikipedia, the free encyclopedia Type of logical system "Predicate logic" redirects here. For logics admitting predicate or function variables, see Higher-order logic . Transformation rules Propositional calculus Rules of inference ( List ) Implication introduction  /  elimination ( modus ponens ) Biconditional introduction  /  elimination Conjunction introduction  /  elimination Disjunction introduction  /  elimination Disjunctive  /  hypothetical syllogism Constructive  /  destructive dil

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