"Bulea logika konkluda sistemo estas sistemo de logiko inventita de brita matematikisto de 19-a jarcento George Boole, kiu provis asimili la malplenan aron, kiu estas, klason de neekzistantaj a\u0135oj, kiel ekzemple rondaj kvadratoj, sen apero de necertaj verecoj. Simile, la subkontrasta rilato estas dissolvita inter la ekzistecaj deklaroj \"iu S estas P\" kaj \"iu S ne estas P\". La unua estas interpretita kiel \"ekzistas iu S tia ke S estas P\" kaj la lasta \"ekzistas iu S tia ke S ne estas P\", kiuj amba\u016D estas klare falsaj se S estas neekzistanta."@eo . . "\u5E03\u5C14\u4E09\u6BB5\u8BBA"@zh . . . "Silog\u00EDstica booliana"@pt . . . . "Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the \"empty set\", that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values. Similarly, the subcontrary relationship is dissolved between the existential statements \"some S is P\" and \"some S is not P\". The former is interpreted as \"there is some S such that S is P\" and the latter, \"there is some S such that S is not P\", both of which are clearly false where S is nonexistent."@en . . . . . "Sillogismo di Boole"@it . . . . . "Bulea logika konkluda sistemo"@eo . . . "1046267293"^^ . . . . . . . "A l\u00F3gica booliana \u00E9 um sistema de l\u00F3gica silog\u00EDstica inventado no s\u00E9culo XIX pelo matem\u00E1tico brit\u00E2nico George Boole, o qual tenta incorporar o \"conjunto vazio\" ( uma classe de entidades inexistentes) sem ter que recorrer a valores de verdade incertos.Na l\u00F3gica booliana, as afirma\u00E7\u00F5es universais \u201Ctodo S \u00E9 P\u201D e \u201Cnenhum S \u00E9 P\u201D, (contr\u00E1rias no esquema aristot\u00E9lico tradicional) podem, de fato, ser simultaneamente verdadeiras desde que o conjunto \"S\" seja vazio.Todo \u201CS \u00E9 P\u201D deve ser entendido como significado que \u201Cn\u00E3o ha nada que seja S e n\u00E3o P ao mesmo tempo\" e \"nenhum S \u00E9 P\" deve ser interpretado como \"n\u00E3o ha nada que seja S e P ao mesmo tempo\". Por exemplo: Uma vez que n\u00E3o existe nada que seja um quadrado redondo, ent\u00E3o \u00E9 verdade que n\u00E3o existe nada que seja um quadrado redondo roxo, e \u00E9 verdade que n\u00E3o existe nada que seja um quadrado redondo n\u00E3o roxo.Deste modo, ambas as declara\u00E7\u00F5es universais s\u00E3o verdadeiras, isto \u00E9, \"todos os quadrados redondos s\u00E3o roxos\" e \"nenhum quadrado redondo \u00E9 roxo\", apesar de n\u00E3o existir quadrado redondo algum. Semelhantemente, a rela\u00E7\u00E3o de subcontrariedade \u00E9 dissolvida entre as afirma\u00E7\u00F5es existenciais \"existe algum S que \u00E9 P\" e \"existe algum S que n\u00E3o \u00E9 P\". O primeiro pode ser interpretado como \"existe algum S tal que S \u00E9 P\" e o segundo como \"existe algum S tal que S n\u00E3o \u00E9 P\". Obviamente, temos que as duas declara\u00E7\u00F5es s\u00E3o falsas se S n\u00E3o existe. Assim a rela\u00E7\u00E3o de subalterna\u00E7\u00E3o entre universal e particular tamb\u00E9m n\u00E3o vale, dado que para um S inexistente, \u201Ctodo S \u00E9 P\" \u00E9 verdade, mas isso n\u00E3o implica que \"algum S \u00E9 P\", que \u00E9 falso. Do quadrado das oposi\u00E7\u00F5es aristot\u00E9lico , apenas a rela\u00E7\u00E3o de contradi\u00E7\u00E3o permanece intacta."@pt . . "Boole's syllogistic"@en . "49460"^^ . . "\u5E03\u5C14\u903B\u8F91\u539F\u6307\u5341\u4E5D\u4E16\u7EAA\u82F1\u56FD\u6570\u5B66\u5BB6\u4E54\u6CBB\u00B7\u5E03\u5C14\u53D1\u660E\u7684\u76F4\u8A00\u4E09\u6BB5\u8BBA\u903B\u8F91\u7CFB\u7EDF\uFF0C\u4ED6\u5C1D\u8BD5\u7ED3\u5408\"\u7A7A\u96C6\"\uFF0C\u5C31\u662F\u8BF4\u4E0D\u5B58\u5728\u7684\u5B9E\u4F53\u7684\u7C7B\uFF0C\u6BD4\u5982\u5706\u56DB\u8FB9\u5F62\uFF0C\u800C\u4E0D\u6C42\u52A9\u4E8E\u4E0D\u53EF\u786E\u5B9A\u7684\u771F\u503C\u3002 \u5728\u5E03\u5C14\u903B\u8F91\u4E2D\uFF0C\u5168\u79F0\u9648\u8FF0\u201C\u6240\u6709 S \u90FD\u662F P\u201D\u548C\u201C\u6CA1\u6709 S \u662F P\u201D(\u5728\u4E9A\u91CC\u58EB\u591A\u5FB7\u65B9\u6848\u4E2D\u662F\u4E0D\u540C\u771F\u7684)\u5728\u5047\u5B9A S \u7684\u96C6\u5408\u662F\u7A7A\u96C6\u7684\u65F6\u5019\u662F\u53EF\u5171\u5B58\u7684\u3002\u201C\u6240\u6709 S \u90FD\u662F P\u201D\u88AB\u89E3\u91CA\u4E3A\u610F\u5473\u7740\u201C\u6CA1\u6709\u4E1C\u897F\u65E2\u662F S \u53C8\u662F\u975E P\u201D\uFF1B\u201C\u6CA1\u6709 S \u662F P\u201D\u5C31\u662F\u8BF4\u201C\u6CA1\u6709\u4E1C\u897F\u65E2\u662F S \u53C8\u662F P\u201D\u3002\u4F8B\u5982\uFF0C\u56E0\u4E3A\u6CA1\u6709\u4E1C\u897F\u662F\u5706\u56DB\u8FB9\u5F62\uFF0C\u6240\u4EE5\u6CA1\u6709\u4E1C\u897F\u662F\u5706\u56DB\u8FB9\u5F62\u5E76\u4E14\u662F\u7D2B\u8272\u7684\uFF0C\u548C\u6CA1\u6709\u4E1C\u897F\u662F\u5706\u56DB\u8FB9\u5F62\u5E76\u4E14\u662F\u975E\u7D2B\u8272\u7684\u4E8C\u8005\u90FD\u662F\u771F\u7684\u3002\u6240\u4EE5\uFF0C\u201C\u6240\u6709\u5706\u56DB\u8FB9\u5F62\u90FD\u662F\u7D2B\u8272\u7684\u201D\u548C\u201C\u6CA1\u6709\u5706\u56DB\u8FB9\u5F62\u662F\u7D2B\u8272\u7684\u201D\uFF0C\u8FD9\u4E24\u4E2A\u5168\u79F0\u9648\u8FF0\u90FD\u662F\u771F\u7684\u3002 \u7C7B\u4F3C\u7684\uFF0C\u5728\u5B58\u5728\u9648\u8FF0\u201C\u6709\u4E9B S \u662F P\u201D\u548C\u201C\u6709\u4E9B S \u4E0D\u662F P\u201D\u4E4B\u95F4\u7684\u4E0D\u540C\u5047\u7684\u8054\u7CFB\u4E5F\u88AB\u6D88\u89E3\u4E86\u3002\u524D\u8005\u88AB\u89E3\u91CA\u4E3A\u201C\u6709\u4E9B\u4E1C\u897F\u65E2 S \u53C8\u662F P\u201D\uFF0C\u540E\u8005\u88AB\u89E3\u91CA\u4E3A\u201C\u6709\u4E9B\u4E1C\u897F\u65E2\u662F S \u53C8\u662F\u975E P\u201D\uFF0C\u5728 S \u4E0D\u5B58\u5728\u7684\u65F6\u5019\u8FD9\u4E8C\u8005\u660E\u663E\u662F\u5047\u7684\u3002 \u6240\u4EE5\uFF0C\u5728\u5168\u79F0\u548C\u5B58\u5728\u9648\u8FF0\u4E4B\u95F4\u7684\u8574\u6DB5\u8054\u7CFB\u4E5F\u4E0D\u518D\u6210\u7ACB\uFF0C\u56E0\u4E3A\u5BF9\u4E8E\u4E00\u4E2A\u4E0D\u5B58\u5728\u7684 S\uFF0C\u4E3A\u771F\u7684\u201C\u6240\u6709 S \u90FD\u662F P\u201D\uFF0C\u4E0D\u8574\u6DB5\u4E3A\u5047\u7684\u201C\u6709\u4E9B S \u662F P\u201D\u3002\u4E9A\u91CC\u58EB\u591A\u5FB7\u7684\u5BF9\u7ACB\u56DB\u8FB9\u5F62\u4E2D\uFF0C\u53EA\u6709\u77DB\u76FE\u8054\u7CFB\u4FDD\u6301\u6709\u6548\u3002"@zh . . "Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the \"empty set\", that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values. In Boolean logic, the universal statements \"all S is P\" and \"no S is P\" (contraries in the traditional Aristotelian schema) are compossible provided that the set of \"S\" is the empty set. \"All S is P\" is construed to mean that \"there is nothing that is both S and not-P\"; \"no S is P\", that \"there is nothing that is both S and P\". For example, since there is nothing that is a round square, it is true both that nothing is a round square and purple, and that nothing is a round square and not-purple. Therefore, both universal statements, that \"all round squares are purple\" and \"no round squares are purple\" are true. Similarly, the subcontrary relationship is dissolved between the existential statements \"some S is P\" and \"some S is not P\". The former is interpreted as \"there is some S such that S is P\" and the latter, \"there is some S such that S is not P\", both of which are clearly false where S is nonexistent. Thus, the subaltern relationship between universal and existential also does not hold, since for a nonexistent S, \"All S is P\" is true but does not entail \"Some S is P\", which is false. Of the Aristotelian square of opposition, only the contradictory relationships remain intact."@en . "Bulea logika konkluda sistemo estas sistemo de logiko inventita de brita matematikisto de 19-a jarcento George Boole, kiu provis asimili la malplenan aron, kiu estas, klason de neekzistantaj a\u0135oj, kiel ekzemple rondaj kvadratoj, sen apero de necertaj verecoj. En bulea logiko, la universalaj deklaroj \"\u0109iu S estas P\" kaj \"neniu S estas P\" (kontrastoj en la tradicia aristotela skemo) estas kune eblaj kondi\u0109e ke la aro de S estas la malplena aro. \"\u0109iu S estas P\" estas konstruita por signifi ke \"ekzistas nenio kiu estas S kaj ne-P\"; \"neniu S estas P\" estas konstruita por \"ekzistas nenio kiu estas kaj S kaj P\". Ekzemple, \u0109ar ekzistas nenio kiu estas ronda kvadrato, estas vere amba\u016D ke nenio estas ronda kvadrato kaj purpura, kaj ke nenio estas ronda kvadrato kaj ne-purpura. Tial, amba\u016D universalaj deklaroj, ke \"\u0109iuj rondaj kvadratoj estas purpuraj\" kaj \"neniuj rondaj kvadratoj estas purpuraj\" estas vera. Simile, la subkontrasta rilato estas dissolvita inter la ekzistecaj deklaroj \"iu S estas P\" kaj \"iu S ne estas P\". La unua estas interpretita kiel \"ekzistas iu S tia ke S estas P\" kaj la lasta \"ekzistas iu S tia ke S ne estas P\", kiuj amba\u016D estas klare falsaj se S estas neekzistanta. Tiel, la subalternaj rilato inter universala\u0135oj kaj ekzistecoj anka\u016D ne veras, \u0109ar por neekzistanta S, \"\u0109iu S estas P\" estas vera sed ne implicas \"iu S estas P\", kio estas falsa. De la aristotela dua potenco de opozicio, nur la malkongruaj rilatoj restas sendifektaj."@eo . . . "2046"^^ . . . "\u5E03\u5C14\u903B\u8F91\u539F\u6307\u5341\u4E5D\u4E16\u7EAA\u82F1\u56FD\u6570\u5B66\u5BB6\u4E54\u6CBB\u00B7\u5E03\u5C14\u53D1\u660E\u7684\u76F4\u8A00\u4E09\u6BB5\u8BBA\u903B\u8F91\u7CFB\u7EDF\uFF0C\u4ED6\u5C1D\u8BD5\u7ED3\u5408\"\u7A7A\u96C6\"\uFF0C\u5C31\u662F\u8BF4\u4E0D\u5B58\u5728\u7684\u5B9E\u4F53\u7684\u7C7B\uFF0C\u6BD4\u5982\u5706\u56DB\u8FB9\u5F62\uFF0C\u800C\u4E0D\u6C42\u52A9\u4E8E\u4E0D\u53EF\u786E\u5B9A\u7684\u771F\u503C\u3002 \u5728\u5E03\u5C14\u903B\u8F91\u4E2D\uFF0C\u5168\u79F0\u9648\u8FF0\u201C\u6240\u6709 S \u90FD\u662F P\u201D\u548C\u201C\u6CA1\u6709 S \u662F P\u201D(\u5728\u4E9A\u91CC\u58EB\u591A\u5FB7\u65B9\u6848\u4E2D\u662F\u4E0D\u540C\u771F\u7684)\u5728\u5047\u5B9A S \u7684\u96C6\u5408\u662F\u7A7A\u96C6\u7684\u65F6\u5019\u662F\u53EF\u5171\u5B58\u7684\u3002\u201C\u6240\u6709 S \u90FD\u662F P\u201D\u88AB\u89E3\u91CA\u4E3A\u610F\u5473\u7740\u201C\u6CA1\u6709\u4E1C\u897F\u65E2\u662F S \u53C8\u662F\u975E P\u201D\uFF1B\u201C\u6CA1\u6709 S \u662F P\u201D\u5C31\u662F\u8BF4\u201C\u6CA1\u6709\u4E1C\u897F\u65E2\u662F S \u53C8\u662F P\u201D\u3002\u4F8B\u5982\uFF0C\u56E0\u4E3A\u6CA1\u6709\u4E1C\u897F\u662F\u5706\u56DB\u8FB9\u5F62\uFF0C\u6240\u4EE5\u6CA1\u6709\u4E1C\u897F\u662F\u5706\u56DB\u8FB9\u5F62\u5E76\u4E14\u662F\u7D2B\u8272\u7684\uFF0C\u548C\u6CA1\u6709\u4E1C\u897F\u662F\u5706\u56DB\u8FB9\u5F62\u5E76\u4E14\u662F\u975E\u7D2B\u8272\u7684\u4E8C\u8005\u90FD\u662F\u771F\u7684\u3002\u6240\u4EE5\uFF0C\u201C\u6240\u6709\u5706\u56DB\u8FB9\u5F62\u90FD\u662F\u7D2B\u8272\u7684\u201D\u548C\u201C\u6CA1\u6709\u5706\u56DB\u8FB9\u5F62\u662F\u7D2B\u8272\u7684\u201D\uFF0C\u8FD9\u4E24\u4E2A\u5168\u79F0\u9648\u8FF0\u90FD\u662F\u771F\u7684\u3002 \u7C7B\u4F3C\u7684\uFF0C\u5728\u5B58\u5728\u9648\u8FF0\u201C\u6709\u4E9B S \u662F P\u201D\u548C\u201C\u6709\u4E9B S \u4E0D\u662F P\u201D\u4E4B\u95F4\u7684\u4E0D\u540C\u5047\u7684\u8054\u7CFB\u4E5F\u88AB\u6D88\u89E3\u4E86\u3002\u524D\u8005\u88AB\u89E3\u91CA\u4E3A\u201C\u6709\u4E9B\u4E1C\u897F\u65E2 S \u53C8\u662F P\u201D\uFF0C\u540E\u8005\u88AB\u89E3\u91CA\u4E3A\u201C\u6709\u4E9B\u4E1C\u897F\u65E2\u662F S \u53C8\u662F\u975E P\u201D\uFF0C\u5728 S \u4E0D\u5B58\u5728\u7684\u65F6\u5019\u8FD9\u4E8C\u8005\u660E\u663E\u662F\u5047\u7684\u3002 \u6240\u4EE5\uFF0C\u5728\u5168\u79F0\u548C\u5B58\u5728\u9648\u8FF0\u4E4B\u95F4\u7684\u8574\u6DB5\u8054\u7CFB\u4E5F\u4E0D\u518D\u6210\u7ACB\uFF0C\u56E0\u4E3A\u5BF9\u4E8E\u4E00\u4E2A\u4E0D\u5B58\u5728\u7684 S\uFF0C\u4E3A\u771F\u7684\u201C\u6240\u6709 S \u90FD\u662F P\u201D\uFF0C\u4E0D\u8574\u6DB5\u4E3A\u5047\u7684\u201C\u6709\u4E9B S \u662F P\u201D\u3002\u4E9A\u91CC\u58EB\u591A\u5FB7\u7684\u5BF9\u7ACB\u56DB\u8FB9\u5F62\u4E2D\uFF0C\u53EA\u6709\u77DB\u76FE\u8054\u7CFB\u4FDD\u6301\u6709\u6548\u3002"@zh . . "A l\u00F3gica booliana \u00E9 um sistema de l\u00F3gica silog\u00EDstica inventado no s\u00E9culo XIX pelo matem\u00E1tico brit\u00E2nico George Boole, o qual tenta incorporar o \"conjunto vazio\" ( uma classe de entidades inexistentes) sem ter que recorrer a valores de verdade incertos.Na l\u00F3gica booliana, as afirma\u00E7\u00F5es universais \u201Ctodo S \u00E9 P\u201D e \u201Cnenhum S \u00E9 P\u201D, (contr\u00E1rias no esquema aristot\u00E9lico tradicional) podem, de fato, ser simultaneamente verdadeiras desde que o conjunto \"S\" seja vazio.Todo \u201CS \u00E9 P\u201D deve ser entendido como significado que \u201Cn\u00E3o ha nada que seja S e n\u00E3o P ao mesmo tempo\" e \"nenhum S \u00E9 P\" deve ser interpretado como \"n\u00E3o ha nada que seja S e P ao mesmo tempo\". Por exemplo: Uma vez que n\u00E3o existe nada que seja um quadrado redondo, ent\u00E3o \u00E9 verdade que n\u00E3o existe nada que seja um quadrado redondo roxo, e \u00E9 verd"@pt .