@prefix owl: . @prefix dbpedia: . dbpedia:Heyting_algebra owl:sameAs . @prefix foaf: . @prefix ns3: . dbpedia:Heyting_algebra foaf:page ns3:Heyting_algebra . @prefix rdfs: . dbpedia:Heyting_algebra rdfs:label "Heyting algebra"@en , "\u6D77\u5EF7\u4EE3\u6570"@zh , "Heyting-Algebra"@de , "Algebra di Heyting"@it , "\u00C1lgebra de Heyting"@es . @prefix dbpprop: . dbpedia:Heyting_algebra dbpprop:abstract "\u5728\u6570\u5B66\u4E2D\uFF0CHeyting \u4EE3\u6570\u662F\u6784\u6210\u5BF9\u5E03\u5C14\u4EE3\u6570\u7684\u63A8\u5E7F\u7684\u7279\u6B8A\u7684\u504F\u5E8F\u96C6\u3002Heyting \u4EE3\u6570\u4E3A\u76F4\u89C9\u903B\u8F91\u800C\u63D0\u51FA\uFF0C\u5B83\u662F\u5728\u5176\u4E2D\u6392\u4E2D\u5F8B\u4E00\u822C\u4E0D\u6210\u7ACB\u7684\u903B\u8F91\u3002\u5B8C\u5168Heyting\u4EE3\u6570\u662F\u65E0\u70B9\u62D3\u6251\u5B66\u7814\u7A76\u7684\u4E2D\u5FC3\u5BF9\u8C61\u3002"@zh , "In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras, named after Arend Heyting. Heyting algebras arise as models of intuitionistic logic, a logic in which the law of excluded middle does not in general hold. Complete Heyting algebras are a central object of study in pointless topology."@en , "In der Mathematik sind Heyting-Algebren spezielle partielle Ordnungen; gleichzeitig ist der Begriff der Heyting-Algebra eine Verallgemeinerung des Begriffs der Boolesche AlgebraBooleschen Algebra. Heyting-Algebren entstehen als Modelle intuitionistische Logikintuitionistischer Logik, einer Logik, in der der Satz vom ausgeschlossenen Dritten im allgemeinen nicht gilt. Vollst\u00E4ndige Heyting-Algebren sind ein zentraler Gegenstand der punktfreien Topologie (Mathematik)Topologie. Die Heyting-Algebra ist nach Arend Heyting benannt."@de , "En matem\u00E1ticas, las \u00E1lgebras de Heyting (Su creador fue Arend Heyting) son conjuntos parcialmente ordenados especiales que constituyen una generalizaci\u00F3n de las \u00E1lgebras de Boole. Las \u00E1lgebras de Heyting se presentan como modelos de la l\u00F3gica intuicionista, una l\u00F3gica en la cual la ley del tercero excluido no vale, en general. Las \u00E1lgebras completas de Heyting son un objeto central de estudio en topolog\u00EDa sin puntos."@es , "Un'algebra di Heyting \u00E8 la struttura di verit\u00E0 della logica intuizionista. Un'algebra di Heyting soddisfa queste propriet\u00E0: chiusura rispetto all'unione (pi\u00F9 in generale, rispetto ad un operatore binario <math>\\vee</math>) e rispetto all'intersezione (operatore binario <math>\\wedge</math>). A differenza dell'algebra di Boole (che rappresente il modo di ragionare in logica classica), non \u00E8 necessariamente chiusa rispetto al complemento (negazione): per cui, ogni algebra di Boole \u00E8 di Heyting. Interpretando delle proposizioni (diciamole A e B) in elementi dell'algebra a e b, l'interpretazione di \"<math>A \\wedge B</math>\" va in <math>a \\wedge_H b</math>, mentre \"<math>A \\vee B</math>\" va in <math>a \\vee_H b</math>. L'interpretazione di <math>A\\to B</math> \u00E8, come si evince dalla definizione stessa, <math>\\bigvee \\{z : z \\wedge a \\le b\\}</math>. Un'algebra di Heyting \u00E8 completa se \u00E8 chiusa rispetto al <math>\\vee</math> numerabile, ovvero rispetto all'implicazione. Esempi di algebre di Heyting complete sono le topologie; una qualsiasi algebra di Heyting pu\u00F2 essere immersa in una topologia costruita ad hoc."@it ; rdfs:comment "En matem\u00E1ticas, las \u00E1lgebras de Heyting (Su creador fue Arend Heyting) son conjuntos parcialmente ordenados especiales que constituyen una generalizaci\u00F3n de las \u00E1lgebras de Boole. Las \u00E1lgebras de Heyting se presentan como modelos de la l\u00F3gica intuicionista, una l\u00F3gica en la cual la ley del tercero excluido no vale, en general. Las \u00E1lgebras completas de Heyting son un objeto central de estudio en topolog\u00EDa sin puntos."@es , "In der Mathematik sind Heyting-Algebren spezielle partielle Ordnungen; gleichzeitig ist der Begriff der Heyting-Algebra eine Verallgemeinerung des Begriffs der Boolesche AlgebraBooleschen Algebra. Heyting-Algebren entstehen als Modelle intuitionistische Logikintuitionistischer Logik, einer Logik, in der der Satz vom ausgeschlossenen Dritten im allgemeinen nicht gilt. Vollst\u00E4ndige Heyting-Algebren sind ein zentraler Gegenstand der punktfreien Topologie (Mathematik)Topologie."@de , "Un'algebra di Heyting \u00E8 la struttura di verit\u00E0 della logica intuizionista. Un'algebra di Heyting soddisfa queste propriet\u00E0: chiusura rispetto all'unione (pi\u00F9 in generale, rispetto ad un operatore binario <math>\\vee</math>) e rispetto all'intersezione (operatore binario <math>\\wedge</math>)."@it , "In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras, named after Arend Heyting. Heyting algebras arise as models of intuitionistic logic, a logic in which the law of excluded middle does not in general hold. Complete Heyting algebras are a central object of study in pointless topology."@en , "\u5728\u6570\u5B66\u4E2D\uFF0CHeyting \u4EE3\u6570\u662F\u6784\u6210\u5BF9\u5E03\u5C14\u4EE3\u6570\u7684\u63A8\u5E7F\u7684\u7279\u6B8A\u7684\u504F\u5E8F\u96C6\u3002Heyting \u4EE3\u6570\u4E3A\u76F4\u89C9\u903B\u8F91\u800C\u63D0\u51FA\uFF0C\u5B83\u662F\u5728\u5176\u4E2D\u6392\u4E2D\u5F8B\u4E00\u822C\u4E0D\u6210\u7ACB\u7684\u903B\u8F91\u3002\u5B8C\u5168Heyting\u4EE3\u6570\u662F\u65E0\u70B9\u62D3\u6251\u5B66\u7814\u7A76\u7684\u4E2D\u5FC3\u5BF9\u8C61\u3002"@zh . @prefix skos: . @prefix ns7: . dbpedia:Heyting_algebra skos:subject ns7:Lattice_theory , ns7:Mathematical_constructivism , ns7:Mathematical_logic . @prefix ns8: . dbpedia:Heyting_algebra dbpprop:hasPhotoCollection ns8:Heyting_algebra . dbpedia:Free_Heyting_algebra dbpprop:redirect dbpedia:Heyting_algebra . dbpedia:Relative_pseudo-complement dbpprop:redirect dbpedia:Heyting_algebra . dbpedia:Heyting_algebras dbpprop:redirect dbpedia:Heyting_algebra .