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**Deduction theorem**— In mathematical logic, the deduction theorem is a metatheorem of first order logic.[1] It is a formalization of the common proof technique in which an implication A → B is proved by assuming A and then proving B from this assumption.… … Wikipedia**deduction theorem**— The theorem provable about some logical systems, that if a conclusion C can be proved from a set of premises A1…An, then there is a proof of An→ C from A1…An–1 … Philosophy dictionary**theorem**— [n] explanation based on hypothesis and experiments assumption, axiom, belief, deduction, dictum, doctrine, formula, fundamental, law, postulate, principium, principle, proposition, rule, statement, theory, thesis; concepts 529,688,689 Ant. fact … New thesaurus**Theorem**— The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements … Wikipedia**theorem**— Synonyms and related words: a priori principle, a priori truth, affirmation, apriorism, assertion, assumed position, assumption, axiom, basis, brocard, categorical proposition, conjecture, data, deduction, dictate, dictum, first principles,… … Moby Thesaurus**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**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**Gödel's completeness theorem**— is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… … Wikipedia**Proof sketch for Gödel's first incompleteness theorem**— This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… … Wikipedia**Löwenheim–Skolem theorem**— In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The… … Wikipedia**Automated theorem proving**— (ATP) or automated deduction, currently the most well developed subfield of automated reasoning (AR), is the proving of mathematical theorems by a computer program. Decidability of the problem Depending on the underlying logic, the problem of… … Wikipedia