@prefix rdf: . @prefix dbpedia: . @prefix ns2: . dbpedia:Craig_interpolation rdf:type ns2:Lemmas . @prefix owl: . dbpedia:Craig_interpolation owl:sameAs . @prefix foaf: . @prefix ns5: . dbpedia:Craig_interpolation foaf:page ns5:Craig_interpolation . @prefix rdfs: . dbpedia:Craig_interpolation rdfs:label "Craig interpolation"@en , "Twierdzenie Craiga"@pl , "\u30AF\u30EC\u30A4\u30B0\u306E\u88DC\u9593\u5B9A\u7406"@ja , "Craig-Interpolation"@de . @prefix dbpprop: . dbpedia:Craig_interpolation dbpprop:abstract "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."@en , "Die Craig-Interpolation ist ein Ausdruck der Logik. Der zugrunde liegende Satz (Craig\u2019s Lemma, Interpolationstheorem) lautet folgenderma\u00DFen: 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."@de , "\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 , "Twierdzenie Craiga jest twierdzeniem logiki, a w szczeg\u00F3lno\u015Bci rachunku predykat\u00F3w pierwszego rz\u0119du). Udowodnione przez Williama Craiga, ameryka\u0144skiego logika."@pl ; rdfs:comment "Die Craig-Interpolation ist ein Ausdruck der Logik. Der zugrunde liegende Satz (Craig\u2019s Lemma, Interpolationstheorem) lautet folgenderma\u00DFen: 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."@de , "Twierdzenie Craiga jest twierdzeniem logiki, a w szczeg\u00F3lno\u015Bci rachunku predykat\u00F3w pierwszego rz\u0119du). Udowodnione przez Williama Craiga, ameryka\u0144skiego logika."@pl , "\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 , "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."@en . @prefix skos: . @prefix ns9: . dbpedia:Craig_interpolation skos:subject ns9:Mathematical_logic , ns9:Lemmas . @prefix ns10: . dbpedia:Craig_interpolation dbpprop:hasPhotoCollection ns10:Craig_interpolation . dbpedia:Interpolation_theorem dbpprop:redirect dbpedia:Craig_interpolation . dbpedia:Craig_Interpolation dbpprop:redirect dbpedia:Craig_interpolation . dbpedia:Craig_interpolation_lemma dbpprop:redirect dbpedia:Craig_interpolation . dbpprop:redirect dbpedia:Craig_interpolation . dbpedia:Craig_reduct dbpprop:redirect dbpedia:Craig_interpolation . @prefix yago: . yago:Craig_interpolation owl:sameAs dbpedia:Craig_interpolation .