Craig interpolation
In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula φ implies a formula ψ, and the two have at least one atomic variable symbol in common, then there is a formula ρ, called an interpolant, such that every non-logical symbol in ρ occurs both in φ and ψ, φ implies ρ, and ρ implies ψ. The theorem was first proved for first-order logic by William Craig in 1957. Variants of the theorem hold for other logics, such as propositional logic. A stronger form of Craig's interpolation theorem for first-order logic was proved by Roger Lyndon in 1959; the overall result is sometimes called the Craig–Lyndon theorem.
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Craig's interpolation lemmaCraig's interpolation theoremCraig's theoremCraig InterpolationCraig interpolation lemmaCraig reductCut-elimination theoremDependence logicIndependence-friendly logicIndex of philosophy articles (A–C)Infinitary logicInstitutional model theoryInterpolation (disambiguation)Interpolation (logic)Interpolation theoremJohann MakowskyJoseph SgroLarisa MaksimovaList of lemmasList of theoremsRobinson's joint consistency theoremRoger LyndonVampire (theorem prover)William Craig (philosopher)
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Craig interpolation
In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula φ implies a formula ψ, and the two have at least one atomic variable symbol in common, then there is a formula ρ, called an interpolant, such that every non-logical symbol in ρ occurs both in φ and ψ, φ implies ρ, and ρ implies ψ. The theorem was first proved for first-order logic by William Craig in 1957. Variants of the theorem hold for other logics, such as propositional logic. A stronger form of Craig's interpolation theorem for first-order logic was proved by Roger Lyndon in 1959; the overall result is sometimes called the Craig–Lyndon theorem.
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En logique mathématique, le th ...... pparaît à la fois dans φ et ψ.
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In mathematical logic, Craig's ...... lled the Craig–Lyndon theorem.
@en
Twierdzenie Craiga – twierdzen ...... (ang.), amerykańskiego logika.
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クレイグの補間定理(英: Craig's interpola ...... 述語論理について証明したのが最初である。クレイグの補題とも。
@ja
크레이그의 보간 정리(Craig's interpolat ...... 로 이 둘을 합쳐 크레이그-린든 정리라 부르기도 한다.
@ko
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En logique mathématique, le th ...... pparaît à la fois dans φ et ψ.
@fr
In mathematical logic, Craig's ...... lled the Craig–Lyndon theorem.
@en
Twierdzenie Craiga – twierdzen ...... (ang.), amerykańskiego logika.
@pl
クレイグの補間定理(英: Craig's interpola ...... 述語論理について証明したのが最初である。クレイグの補題とも。
@ja
크레이그의 보간 정리(Craig's interpolat ...... 로 이 둘을 합쳐 크레이그-린든 정리라 부르기도 한다.
@ko
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Craig interpolation
@en
Craig-Interpolation
@de
Théorème d'interpolation de Craig
@fr
Twierdzenie Craiga
@pl
クレイグの補間定理
@ja
크레이그의 보간 정리
@ko