provable sequent

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• Sequent calculus — In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi, systems LK and LJ, were introduced by Gerhard Gentzen in 1934 as …   Wikipedia

• Sequent — In proof theory, a sequent is a formalized statement of provability that is frequently used when specifying calculi for deduction. In the sequent calculus, the name sequent is used for the construct which can be regarded as a specific kind of… …   Wikipedia

• Natural deduction — In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the natural way of reasoning. This contrasts with the axiomatic systems which instead use… …   Wikipedia

• Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …   Wikipedia

• 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

• Intuitionistic logic — Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well formed statements are assumed to be either true or… …   Wikipedia

• Rule of inference — In logic, a rule of inference (also called a transformation rule) is a function from sets of formulae to formulae. The argument is called the premise set (or simply premises ) and the value the conclusion . They can also be viewed as relations… …   Wikipedia

• Cut-elimination theorem — The cut elimination theorem (or Gentzen s Hauptsatz) is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen 1934 in his landmark paper Investigations in Logical Deduction for the… …   Wikipedia

• Curry–Howard correspondence — A proof written as a functional program: the proof of commutativity of addition on natural numbers in the proof assistant Coq. nat ind stands for mathematical induction, eq ind for substitution of equals and f equal for taking the same function… …   Wikipedia

• Herbrand's theorem — is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). [J. Herbrand: Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et des Lettres de Varsovie, Class III, Sciences Mathematiques et… …   Wikipedia

• Proof theory — is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as plain lists, boxed… …   Wikipedia