derivable 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
Admissible rule — In logic, a rule of inference is admissible in a formal system if the set of theorems of the system is closed under the rule. The concept of an admissible rule was introduced by Paul Lorenzen (1955).DefinitionsThe concept of admissibility, as… … 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
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
Paraconsistent logic — A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (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
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
Relevance logic — Relevance logic, also called relevant logic, is a kind of non classical logic requiring the antecedent and consequent of implications be relevantly related. They may be viewed as a family of substructural or modal logics. (It is generally, but… … Wikipedia
Hilbert-style deduction system — In logic, especially mathematical logic, a Hilbert style deduction system is a type of system of formal deduction attributed to Gottlob FregeMáté Ruzsa 1997:129] and David Hilbert. These deductive systems are most often studied for first order… … Wikipedia
Effect — (Roget s Thesaurus) >Constant sequent. < N PARAG:Effect >N GRP: N 1 Sgm: N 1 effect effect consequence Sgm: N 1 aftergrowth aftergrowth aftercome Sgm: N 1 derivative derivative derivation Sgm: N 1 result result … English dictionary for students
