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# first-order logic

The study of inference in first-order languages.

Philosophy dictionary. . 2011.

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• First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …   Wikipedia

• first-order logic — noun A formal deductive system extended from propositional logic with the possibility to quantify over individuals of the domain of discourse. Syn: FOL …   Wiktionary

• First Order Logic —   A technique for organising propositions and making relationships between the propositions in an expert system. See also Expert system …   International financial encyclopaedia

• First-order reduction — A first order reduction is a very weak type of reduction between two computational problems in computational complexity theory. A first order reduction is a reduction where each component is restricted to be in the class FO of problems calculable …   Wikipedia

• Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic. Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …   Wikipedia

• Higher-order logic — In mathematics, higher order logic is distinguished from first order logic in a number of ways.One of these is the type of variables appearing in quantifications; in first order logic, roughly speaking, it is forbidden to quantify over predicates …   Wikipedia

• Zeroth-order logic — is a term for a quantifier free fragment of first order logic.A finitely axiomatizable zeroth order logic is isomorphic to a propositional logic. Zeroth order logic can transcend the power of propositional logic if axiom schemata are allowed. An… …   Wikipedia

• higher-order logic — One in which the variables of the quantifiers are permitted to range over properties and functions as well as individuals (see also first order language ) …   Philosophy dictionary

• List of first-order theories — In mathematical logic, a first order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties. PreliminariesFor every natural mathematical structure… …   Wikipedia

• International Workshop on First-Order Theorem Proving — The International Workshop on First Order Theorem Proving (FTP) is a scientific meeting of researchers interested in automated theorem proving for first order logic and related fields. FTP workshops are less formal than many conferences, but more …   Wikipedia