. . "Die Craig-Interpolation ist ein Ausdruck der Logik. Der zugrunde liegende Satz (Craig\u2019s Lemma, Interpolationstheorem) lautet folgenderma\u00DFen: Es seien und zwei Theorien und der Satz sei ein in ableitbarer Satz. Dann gilt: Es gibt ein , sodass in ableitbar ist, und ist in ableitbar."@de . "Twierdzenie Craiga \u2013 twierdzenie logiki, a w szczeg\u00F3lno\u015Bci rachunku predykat\u00F3w pierwszego rz\u0119du. Udowodnione przez (ang.), ameryka\u0144skiego logika."@pl . . "\uD06C\uB808\uC774\uADF8\uC758 \uBCF4\uAC04 \uC815\uB9AC"@ko . . . . . "En logique math\u00E9matique, le th\u00E9or\u00E8me d'interpolation de Craig dit que si une formule \u03C6 en implique une deuxi\u00E8me \u03C8, et que \u03C6 et \u03C8 partagent au moins un symbole non logique en commun, alors il existe une formule \u03C1, appel\u00E9e interpolant, telle que : \n* \u03C6 implique \u03C1 ; \n* \u03C1 implique \u03C8 ; \n* tout symbole non logique dans \u03C1 appara\u00EEt \u00E0 la fois dans \u03C6 et \u03C8."@fr . . . . . . . . . "Die Craig-Interpolation ist ein Ausdruck der Logik. Der zugrunde liegende Satz (Craig\u2019s Lemma, Interpolationstheorem) lautet folgenderma\u00DFen: Es seien und zwei Theorien und der Satz sei ein in ableitbarer Satz. Dann gilt: Es gibt ein , sodass in ableitbar ist, und ist in ableitbar."@de . . . . "Craig-Interpolation"@de . . "Craig interpolation"@en . "\uD06C\uB808\uC774\uADF8\uC758 \uBCF4\uAC04 \uC815\uB9AC(Craig's interpolation theorem, -\u88DC\u9593 \u5B9A\u7406)\uB294 \uC99D\uBA85 \uC774\uB860\uC758 \uC815\uB9AC\uB85C, \uBBF8\uAD6D\uC758 \uCCA0\uD559\uC790\uC774\uC790 \uB17C\uB9AC\uD559\uC790\uC778 \uAC00 \uC81C\uC2DC\uD558\uC600\uB2E4. \uAC04\uB2E8\uD788 \uB9D0\uD574 \uB2E4\uC74C\uACFC \uAC19\uC774 \uC4F8 \uC218 \uC788\uB2E4. \n* \uC5B4\uB5A4 \uB17C\uB9AC\uC2DD a\uC5D0\uC11C \uB2E4\uB978 \uB17C\uB9AC\uC2DD b\uB97C \uCD94\uB860\uD560 \uC218 \uC788\uB2E4\uACE0 \uD558\uC790. \uADF8\uB7EC\uBA74, c\uC5D0\uC11C \uB098\uD0C0\uB098\uB294 \uBAA8\uB4E0 \uB294 a\uC640 b \uAC01\uAC01\uC5D0\uC11C\uB3C4 \uB098\uD0C0\uB098\uB294 \uC81C3\uC758 \uB17C\uB9AC\uC2DD c\uAC00 \uC874\uC7AC\uD558\uC5EC a\uC5D0\uC11C c\uB97C \uCD94\uB860\uD560 \uC218 \uC788\uACE0, \uB2E4\uC2DC c\uC5D0\uC11C b\uB97C \uCD94\uB860\uD560 \uC218 \uC788\uB2E4. \uC774 c\uB97C \uBCF4\uAC04(interpolant)\uC774\uB77C \uD55C\uB2E4. \uD06C\uB808\uC774\uADF8\uB294 1957\uB144 \uC774 \uC815\uB9AC\uB97C \uC77C\uCC28 \uB17C\uB9AC\uD559\uC5D0 \uB300\uD574 \uC99D\uBA85\uD558\uC600\uB2E4. \uBBF8\uAD6D \uC218\uD559\uC790 \uC774 \uC77C\uCC28 \uB17C\uB9AC\uD559\uC5D0 \uB300\uD55C \uC774 \uC815\uB9AC\uC758 \uBCF4\uB2E4 \uAC15\uD55C \uD310\uBCF8\uC744 1959\uB144 \uC99D\uBA85\uD558\uC600\uC73C\uBBC0\uB85C \uC774 \uB458\uC744 \uD569\uCCD0 \uD06C\uB808\uC774\uADF8-\uB9B0\uB4E0 \uC815\uB9AC\uB77C \uBD80\uB974\uAE30\uB3C4 \uD55C\uB2E4."@ko . . . . . . . "\u30AF\u30EC\u30A4\u30B0\u306E\u88DC\u9593\u5B9A\u7406\uFF08\u82F1: Craig's interpolation theorem\uFF09\u306F\u8AD6\u7406\u5B66\u306B\u304A\u3051\u308B\u5B9A\u7406\u3067\u3042\u308A\u3001\u8AD6\u7406\u4F53\u7CFB\u306B\u3088\u3063\u3066\u305D\u306E\u5B9A\u7FA9\u304C\u7570\u306A\u308B\u3002William Craig \u304C1957\u5E74\u3001\u4E00\u968E\u8FF0\u8A9E\u8AD6\u7406\u306B\u3064\u3044\u3066\u8A3C\u660E\u3057\u305F\u306E\u304C\u6700\u521D\u3067\u3042\u308B\u3002\u30AF\u30EC\u30A4\u30B0\u306E\u88DC\u984C\u3068\u3082\u3002"@ja . . . "\u30AF\u30EC\u30A4\u30B0\u306E\u88DC\u9593\u5B9A\u7406"@ja . . . "1059769235"^^ . . . . . . . "Th\u00E9or\u00E8me d'interpolation de Craig"@fr . "2056790"^^ . "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 \u03C6 implies a formula \u03C8, and the two have at least one atomic variable symbol in common, then there is a formula \u03C1, called an interpolant, such that every non-logical symbol in \u03C1 occurs both in \u03C6 and \u03C8, \u03C6 implies \u03C1, and \u03C1 implies \u03C8. 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\u2013Lyndon theorem."@en . . "\u30AF\u30EC\u30A4\u30B0\u306E\u88DC\u9593\u5B9A\u7406\uFF08\u82F1: Craig's interpolation theorem\uFF09\u306F\u8AD6\u7406\u5B66\u306B\u304A\u3051\u308B\u5B9A\u7406\u3067\u3042\u308A\u3001\u8AD6\u7406\u4F53\u7CFB\u306B\u3088\u3063\u3066\u305D\u306E\u5B9A\u7FA9\u304C\u7570\u306A\u308B\u3002William Craig \u304C1957\u5E74\u3001\u4E00\u968E\u8FF0\u8A9E\u8AD6\u7406\u306B\u3064\u3044\u3066\u8A3C\u660E\u3057\u305F\u306E\u304C\u6700\u521D\u3067\u3042\u308B\u3002\u30AF\u30EC\u30A4\u30B0\u306E\u88DC\u984C\u3068\u3082\u3002"@ja . . "\uD06C\uB808\uC774\uADF8\uC758 \uBCF4\uAC04 \uC815\uB9AC(Craig's interpolation theorem, -\u88DC\u9593 \u5B9A\u7406)\uB294 \uC99D\uBA85 \uC774\uB860\uC758 \uC815\uB9AC\uB85C, \uBBF8\uAD6D\uC758 \uCCA0\uD559\uC790\uC774\uC790 \uB17C\uB9AC\uD559\uC790\uC778 \uAC00 \uC81C\uC2DC\uD558\uC600\uB2E4. \uAC04\uB2E8\uD788 \uB9D0\uD574 \uB2E4\uC74C\uACFC \uAC19\uC774 \uC4F8 \uC218 \uC788\uB2E4. \n* \uC5B4\uB5A4 \uB17C\uB9AC\uC2DD a\uC5D0\uC11C \uB2E4\uB978 \uB17C\uB9AC\uC2DD b\uB97C \uCD94\uB860\uD560 \uC218 \uC788\uB2E4\uACE0 \uD558\uC790. \uADF8\uB7EC\uBA74, c\uC5D0\uC11C \uB098\uD0C0\uB098\uB294 \uBAA8\uB4E0 \uB294 a\uC640 b \uAC01\uAC01\uC5D0\uC11C\uB3C4 \uB098\uD0C0\uB098\uB294 \uC81C3\uC758 \uB17C\uB9AC\uC2DD c\uAC00 \uC874\uC7AC\uD558\uC5EC a\uC5D0\uC11C c\uB97C \uCD94\uB860\uD560 \uC218 \uC788\uACE0, \uB2E4\uC2DC c\uC5D0\uC11C b\uB97C \uCD94\uB860\uD560 \uC218 \uC788\uB2E4. \uC774 c\uB97C \uBCF4\uAC04(interpolant)\uC774\uB77C \uD55C\uB2E4. \uD06C\uB808\uC774\uADF8\uB294 1957\uB144 \uC774 \uC815\uB9AC\uB97C \uC77C\uCC28 \uB17C\uB9AC\uD559\uC5D0 \uB300\uD574 \uC99D\uBA85\uD558\uC600\uB2E4. \uBBF8\uAD6D \uC218\uD559\uC790 \uC774 \uC77C\uCC28 \uB17C\uB9AC\uD559\uC5D0 \uB300\uD55C \uC774 \uC815\uB9AC\uC758 \uBCF4\uB2E4 \uAC15\uD55C \uD310\uBCF8\uC744 1959\uB144 \uC99D\uBA85\uD558\uC600\uC73C\uBBC0\uB85C \uC774 \uB458\uC744 \uD569\uCCD0 \uD06C\uB808\uC774\uADF8-\uB9B0\uB4E0 \uC815\uB9AC\uB77C \uBD80\uB974\uAE30\uB3C4 \uD55C\uB2E4."@ko . "Twierdzenie Craiga"@pl . . "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 \u03C6 implies a formula \u03C8, and the two have at least one atomic variable symbol in common, then there is a formula \u03C1, called an interpolant, such that every non-logical symbol in \u03C1 occurs both in \u03C6 and \u03C8, \u03C6 implies \u03C1, and \u03C1 implies \u03C8. 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\u2013Lyndon theorem."@en . . . . . . . . . . . . . . . . . "8193"^^ . . . "Twierdzenie Craiga \u2013 twierdzenie logiki, a w szczeg\u00F3lno\u015Bci rachunku predykat\u00F3w pierwszego rz\u0119du. Udowodnione przez (ang.), ameryka\u0144skiego logika."@pl . . . . . . . . . . . . "En logique math\u00E9matique, le th\u00E9or\u00E8me d'interpolation de Craig dit que si une formule \u03C6 en implique une deuxi\u00E8me \u03C8, et que \u03C6 et \u03C8 partagent au moins un symbole non logique en commun, alors il existe une formule \u03C1, appel\u00E9e interpolant, telle que : \n* \u03C6 implique \u03C1 ; \n* \u03C1 implique \u03C8 ; \n* tout symbole non logique dans \u03C1 appara\u00EEt \u00E0 la fois dans \u03C6 et \u03C8."@fr . . . . .