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 then there is a third formula ρ, called an interpolant, such that every nonlogical 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.

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  • 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 then there is a third formula ρ, called an interpolant, such that every nonlogical 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 theorem for first-order logic was proved by Roger Lyndon in 1959; the overall result is sometimes called the Craig–Lyndon theorem.
  • Die Craig-Interpolation ist ein Ausdruck der Logik. Der zugrunde liegende Satz (Craig’s Lemma, Interpolationstheorem) lautet folgendermaßen: Es seien <math> T1</math> und <math> T2</math> zwei Theorien und der Satz <math> A \rightarrow C </math> sei ein in <math> T1 \cup T2 </math> ableitbarer Satz. Dann gilt: Es gibt ein <math> B</math> mit <math> A \rightarrow B </math> in <math> T1 </math> ableitbar und <math> B \rightarrow C</math> ist in <math> T2 </math> ableitbar.
  • クレイグの補間定理（英: Craig's interpolation theorem）は論理学における定理であり、論理体系によってその定義が異なる。William Craig が1957年、一階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。
  • Twierdzenie Craiga jest twierdzeniem logiki, a w szczególności rachunku predykatów pierwszego rzędu). Udowodnione przez Williama Craiga, amerykańskiego logika.
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  • 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 then there is a third formula ρ, called an interpolant, such that every nonlogical 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.
  • Die Craig-Interpolation ist ein Ausdruck der Logik. Der zugrunde liegende Satz (Craig’s Lemma, Interpolationstheorem) lautet folgendermaßen: Es seien <math> T1</math> und <math> T2</math> zwei Theorien und der Satz <math> A \rightarrow C </math> sei ein in <math> T1 \cup T2 </math> ableitbarer Satz.
  • クレイグの補間定理（英: Craig's interpolation theorem）は論理学における定理であり、論理体系によってその定義が異なる。William Craig が1957年、一階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。
  • Twierdzenie Craiga jest twierdzeniem logiki, a w szczególności rachunku predykatów pierwszego rzędu). Udowodnione przez Williama Craiga, amerykańskiego logika.
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  • Craig interpolation
  • Craig-Interpolation
  • クレイグの補間定理
  • Twierdzenie Craiga
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