. . . "En l\u00F2gica booleana, una f\u00F3rmula est\u00E0 en forma normal conjuntiva (FNC) si correspon a una conjunci\u00F3 de cl\u00E0usules, on una cl\u00E0usula \u00E9s una disjunci\u00F3 de , on un literal i el seu complement no poden apar\u00E8ixer en la mateixa cl\u00E0usula. Aquesta definici\u00F3 \u00E9s similar a la de emprades en teoria de circuits."@ca . . . "Conjunctive normal form"@en . . "\u5408\u53D6\u8303\u5F0F"@zh . "Na l\u00F3gica booleana, uma f\u00F3rmula est\u00E1 na forma normal conjuntiva (FNC) se \u00E9 uma conjun\u00E7\u00E3o de cl\u00E1usulas, onde uma cl\u00E1usula \u00E9 uma disjun\u00E7\u00E3o de literais. Sendo uma forma normal, a FNC \u00E9 \u00FAtil em . Ela \u00E9 similar \u00E0 usada na teoria dos circuitos. Por exemplo, todas as f\u00F3rmulas seguintes est\u00E3o na FNC: : Por\u00E9m, as seguintes f\u00F3rmulas n\u00E3o est\u00E3o: As tr\u00EAs f\u00F3rmulas acima s\u00E3o equivalentes respectivamente \u00E0s tr\u00EAs f\u00F3rmulas seguintes que est\u00E3o na forma normal conjuntiva: A seguinte f\u00F3rmula \u00E9 uma gram\u00E1tica formal para FNC: 1. \u2192 \u22282. \u2192 \u22273. \u2192 \u00AC4. \u2192 5. \u2192 6. \u2192 7. \u21928. \u2192 9. \u2192 Onde \u00E9 qualquer vari\u00E1vel."@pt . "\uBD88 \uB300\uC218\uC5D0\uC11C \uB17C\uB9AC\uACF1 \uD45C\uC900\uD615(conjunctive normal form)\uC740 \uC758 \uB17C\uB9AC\uACF1\uC73C\uB85C \uB098\uD0C0\uB0B8 \uB17C\uB9AC\uC2DD\uC744 \uB9D0\uD55C\uB2E4. \uC5EC\uAE30\uC11C \uC808\uC740 \uC758 \uB17C\uB9AC\uD569\uC73C\uB85C \uC774\uB8E8\uC5B4\uC9C4\uB2E4. \uB17C\uB9AC\uACF1 \uD45C\uC900\uD615\uC758 \uC601\uBB38 \uD45C\uAE30\uB97C \uC904\uC5EC\uC11C CNF\uB77C\uACE0\uB3C4 \uD55C\uB2E4. CNF\uC640 \uBC18\uB300\uB85C \uB9AC\uD130\uB7F4\uC758 \uB17C\uB9AC\uACF1\uC73C\uB85C \uC774\uB8E8\uC5B4\uC9C4 \uC808\uB4E4\uC744 \uB17C\uB9AC\uD569\uC73C\uB85C \uC5F0\uACB0\uD560 \uC218\uB3C4 \uC788\uB2E4. \uC774\uB97C \uC774\uB77C\uACE0 \uD55C\uB2E4. \uBAA8\uB4E0 \uBA85\uC81C \uB17C\uB9AC\uC2DD\uC740 \uB3D9\uB4F1\uD55C CNF\uB85C \uBCC0\uD658\uB420 \uC218 \uC788\uB2E4. \uC774 \uBCC0\uD658\uC740 \uC774\uC911\uBD80\uC815 \uBC95\uCE59, \uB4DC\uBAA8\uB974\uAC04 \uBC95\uCE59, \uBD84\uBC30 \uBC95\uCE59 \uB4F1\uC744 \uC368\uC11C \uC774\uB8E8\uC5B4\uC9C4\uB2E4. \uB9AC\uD130\uB7F4\uC758 \uAC1C\uC218\uAC00 3\uAC1C \uC774\uD558\uB85C \uC81C\uD55C\uB41C CNF\uB97C 3-CNF\uB77C\uACE0 \uD558\uBA70 \uACC4\uC0B0 \uC774\uB860\uC5D0\uC11C \uC911\uC694\uD558\uAC8C \uB2E4\uB8E8\uC5B4\uC9C4\uB2E4. \uB2E4\uB978 \uAC1C\uC218\uB85C \uC81C\uD55C\uD560 \uB54C\uB3C4 \uB9C8\uCC2C\uAC00\uC9C0\uB85C \uC815\uC758\uD560 \uC218 \uC788\uC73C\uB098 2-CNF, 3-CNF \uC774\uC678\uC5D0\uB294 \uC911\uC694\uD558\uAC8C \uB2E4\uB8E8\uC9C0 \uC54A\uB294\uB2E4."@ko . "\u041A\u043E\u043D\u044A\u044E\u043D\u043A\u0442\u0438\u0432\u043D\u0430\u044F \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430\u044F \u0444\u043E\u0440\u043C\u0430"@ru . . "\u041A\u043E\u043D'\u044E\u043D\u043A\u0442\u0438\u0432\u043D\u0430 \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430 \u0444\u043E\u0440\u043C\u0430"@uk . . . "Conjunctive normal form"@en . . . "En l\u00F3gica booleana, una f\u00F3rmula est\u00E1 en forma normal conjuntiva (FNC) si corresponde a una conjunci\u00F3n de cl\u00E1usulas, donde una cl\u00E1usula es una disyunci\u00F3n de literales, donde un literal y su complemento no pueden aparecer en la misma cl\u00E1usula. Esta definici\u00F3n es similar a la de forma de productos de sumas usadas en teor\u00EDa de circuitos. Todas las conjunciones de literales y todas las disyunciones de literales est\u00E1n en FNC, puesto que pueden ser vistas, respectivamente, como conjunciones de cl\u00E1usulas de un literal, y como conjunciones de una \u00FAnica cl\u00E1usula. Al igual que en una forma normal disyuntiva (FND), los \u00FAnicos conectivos l\u00F3gicos que pueden aparecer en una f\u00F3rmula en FNC son la conjunci\u00F3n, disyunci\u00F3n y negaci\u00F3n. El operador negaci\u00F3n solo puede aplicarse a un literal, y no a una cl\u00E1usula completa, lo que significa que este s\u00F3lo puede preceder a una variable proposicional o un s\u00EDmbolo de predicado. En demostraci\u00F3n autom\u00E1tica de teoremas, la noci\u00F3n de \u00ABforma normal clausal\u00BB se utiliza frecuentemente en un sentido m\u00E1s estricto, significando una representaci\u00F3n particular de una f\u00F3rmula FNC como un conjunto de conjuntos de literales."@es . . . "En l\u00F2gica booleana, una f\u00F3rmula est\u00E0 en forma normal conjuntiva (FNC) si correspon a una conjunci\u00F3 de cl\u00E0usules, on una cl\u00E0usula \u00E9s una disjunci\u00F3 de , on un literal i el seu complement no poden apar\u00E8ixer en la mateixa cl\u00E0usula. Aquesta definici\u00F3 \u00E9s similar a la de emprades en teoria de circuits. Totes les conjuncions de literals i totes les disjuncions de literals estan en FNC, car poden ser vistes, respectivament, com a conjuncions de cl\u00E0usules d'un literal, i com a conjuncions d'una \u00FAnica cl\u00E0usula. De la mateixa manera que en forma normal disjuntiva (FND), els \u00FAnics connectors l\u00F2gics que poden apar\u00E8ixer en una f\u00F3rmula en FNC s\u00F3n la conjunci\u00F3, la disjunci\u00F3 i la negaci\u00F3. L'operador negaci\u00F3 nom\u00E9s pot aplicar-se a un literal, i no a una cl\u00E0usula completa, la qual cosa significa que nom\u00E9s pot precedir una ."@ca . . "\u5728\u5E03\u5C14\u903B\u8F91\u4E2D\uFF0C\u5982\u679C\u4E00\u4E2A\u516C\u5F0F\u662F\u5B50\u53E5\u7684\u5408\u53D6\uFF0C\u90A3\u4E48\u5B83\u662F\u5408\u53D6\u8303\u5F0F(CNF)\u7684\u3002\u4F5C\u4E3A\u89C4\u8303\u5F62\u5F0F\uFF0C\u5B83\u5728\u81EA\u52A8\u5B9A\u7406\u8BC1\u660E\u4E2D\u6709\u7528\u3002\u5B83\u7C7B\u4F3C\u4E8E\u5728\u7535\u8DEF\u7406\u8BBA\u4E2D\u7684\u3002 \u6240\u6709\u7684\u6587\u5B57\u7684\u5408\u53D6\u548C\u6240\u6709\u7684\u6587\u5B57\u7684\u6790\u53D6\u662F CNF \u7684\uFF0C\u56E0\u4E3A\u53EF\u4EE5\u88AB\u5206\u522B\u770B\u4F5C\u4E00\u4E2A\u6587\u5B57\u7684\u5B50\u53E5\u7684\u5408\u53D6\u548C\u6790\u53D6\u3002\u548C\u6790\u53D6\u8303\u5F0F(DNF)\u4E2D\u4E00\u6837\uFF0C\u5728 CNF \u516C\u5F0F\u4E2D\u53EF\u4EE5\u5305\u542B\u7684\u547D\u9898\u8FDE\u7ED3\u8BCD\u662F\u4E0E\u3001\u6216\u548C\u975E\u3002\u975E\u7B97\u5B50\u53EA\u80FD\u7528\u505A\u6587\u5B57\u7684\u4E00\u90E8\u5206\uFF0C\u8FD9\u610F\u5473\u7740\u5B83\u53EA\u80FD\u5728\u547D\u9898\u53D8\u91CF\u524D\u51FA\u73B0\u3002 \u4F8B\u5982\uFF0C\u4E0B\u5217\u6240\u6709\u516C\u5F0F\u90FD\u662F CNF: \u800C\u4E0B\u5217\u4E0D\u662F: \u4E0A\u8FF0\u4E09\u4E2A\u516C\u5F0F\u5206\u522B\u7B49\u4EF7\u4E8E\u5408\u53D6\u8303\u5F0F\u7684\u4E0B\u5217\u4E09\u4E2A\u516C\u5F0F: \u6240\u6709\u547D\u9898\u516C\u5F0F\u90FD\u53EF\u4EE5\u8F6C\u6362\u6210 CNF \u7684\u7B49\u4EF7\u516C\u5F0F\u3002\u8FD9\u79CD\u53D8\u6362\u57FA\u4E8E\u4E86\u5173\u4E8E\u903B\u8F91\u7B49\u4EF7\u7684\u89C4\u5219: \u53CC\u91CD\u5426\u5B9A\u5F8B\u3001\u5FB7\u00B7\u6469\u6839\u5B9A\u5F8B\u548C\u5206\u914D\u5F8B\u3002 \u56E0\u4E3A\u6240\u6709\u903B\u8F91\u516C\u5F0F\u90FD\u53EF\u4EE5\u8F6C\u6362\u6210\u5408\u53D6\u8303\u5F0F\u7684\u7B49\u4EF7\u516C\u5F0F\uFF0C\u8BC1\u660E\u7ECF\u5E38\u57FA\u4E8E\u6240\u6709\u516C\u5F0F\u90FD\u662F CNF \u7684\u5047\u5B9A\u3002\u4F46\u662F\u5728\u67D0\u4E9B\u60C5\u51B5\u4E0B\uFF0C\u8FD9\u79CD\u5230 CNF \u7684\u8F6C\u6362\u53EF\u80FD\u5BFC\u81F4\u516C\u5F0F\u7684\u6307\u6570\u6027\u7206\u6DA8\u3002\u4F8B\u5982\uFF0C\u628A\u4E0B\u8FF0\u975E-CNF \u516C\u5F0F\u8F6C\u6362\u6210 CNF \u751F\u6210\u6709 \u4E2A\u5B50\u53E5\u7684\u516C\u5F0F:"@zh . . . . . . . . . "\u041A\u043E\u043D'\u044E\u043D\u043A\u0442\u0438\u0301\u0432\u043D\u0430 \u043D\u043E\u0440\u043C\u0430\u0301\u043B\u044C\u043D\u0430 \u0444\u043E\u0301\u0440\u043C\u0430 (\u041A\u041D\u0424) \u0432 \u0431\u0443\u043B\u0435\u0432\u0456\u0439 \u043B\u043E\u0433\u0456\u0446\u0456 - \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430 \u0444\u043E\u0440\u043C\u0430 \u0432 \u044F\u043A\u0456\u0439 \u0431\u0443\u043B\u0435\u0432\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u043C\u0430\u0454 \u0432\u0438\u0434 \u043A\u043E\u043D'\u044E\u043D\u043A\u0446\u0456\u0457 \u0434\u0435\u043A\u0456\u043B\u044C\u043A\u043E\u0445 \u0434\u0438\u0437'\u044E\u043D\u043A\u0442\u0456\u0432 (\u0434\u0435 \u0434\u0438\u0437'\u044E\u043D\u043A\u0442\u0430\u043C\u0438 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C\u0441\u044F \u0434\u0438\u0437'\u044E\u043D\u043A\u0446\u0456\u0457 \u0434\u0435\u043A\u0456\u043B\u044C\u043A\u043E\u0445 \u043F\u0440\u043E\u043F\u043E\u0437\u0438\u0446\u0456\u0439\u043D\u0438\u0445 \u0441\u0438\u043C\u0432\u043E\u043B\u0456\u0432 \u0430\u0431\u043E \u0457\u0445 \u0437\u0430\u043F\u0435\u0440\u0435\u0447\u0435\u043D\u044C). \u041A\u043E\u043D'\u044E\u043D\u043A\u0442\u0438\u0432\u043D\u0430 \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430 \u0444\u043E\u0440\u043C\u0430 \u0448\u0438\u0440\u043E\u043A\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0432 \u0430\u0432\u0442\u043E\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u0456 \u0442\u0435\u043E\u0440\u0435\u043C, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u0432\u043E\u043D\u0430 \u0454 \u043E\u0441\u043D\u043E\u0432\u043E\u044E \u0434\u043B\u044F \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u0430\u043D\u043D\u044F \u043F\u0440\u0430\u0432\u0438\u043B\u0430 \u0440\u0435\u0437\u043E\u043B\u044E\u0446\u0456\u0457."@uk . . . "Forma normal conjuntiva"@pt . . "\u9023\u8A00\u6A19\u6E96\u5F62"@ja . . . "Forme normale conjonctive"@fr . . "Als konjunktive Normalform (kurz KNF, englisch CNF f\u00FCr conjunctive normal form) wird in der Aussagenlogik eine bestimmte Form von Formeln bezeichnet."@de . . "Nella logica booleana, una formula \u00E8 in forma normale congiuntiva o congiunta (FNC), indicata anche come CNF (acronimo di Conjunctive Normal Form) se \u00E8 una congiunzione di clausole, dove le clausole sono una disgiunzione di letterali. Una formula in CNF ha quindi la seguente struttura: : Numero di clausole. : Numero di letterali della clausola i-esima. : \u00C8 il k-esimo letterale della i-esima clausola. Un letterale pu\u00F2 essere una variabile booleana (cio\u00E8 che pu\u00F2 valere solo 0 o 1, vero o falso) o la negazione di una variabile."@it . . . . . . . . "Konjunktivn\u00ED norm\u00E1ln\u00ED forma"@cs . "En l\u00F3gica booleana, una f\u00F3rmula est\u00E1 en forma normal conjuntiva (FNC) si corresponde a una conjunci\u00F3n de cl\u00E1usulas, donde una cl\u00E1usula es una disyunci\u00F3n de literales, donde un literal y su complemento no pueden aparecer en la misma cl\u00E1usula. Esta definici\u00F3n es similar a la de forma de productos de sumas usadas en teor\u00EDa de circuitos. En demostraci\u00F3n autom\u00E1tica de teoremas, la noci\u00F3n de \u00ABforma normal clausal\u00BB se utiliza frecuentemente en un sentido m\u00E1s estricto, significando una representaci\u00F3n particular de una f\u00F3rmula FNC como un conjunto de conjuntos de literales."@es . . . "Vev\u00FDrokov\u00E9 logice je formule v konjunktivn\u00ED norm\u00E1ln\u00ED form\u011B (KNF nebo CNF z anglick\u00E9ho conjunctive normal form), pokud je ve tvaru konjunkc\u00ED , kde klauzuli definujeme jako disjunkci (a je-li v\u00FDrokov\u00E1 prom\u011Bnn\u00E1, tak j\u00ED ur\u010Den\u00E9 liter\u00E1ly jsou pr\u00E1v\u011B a ). Jako norm\u00E1ln\u00ED forma se pou\u017E\u00EDv\u00E1 v . Podobn\u00E1 kanonick\u00E1 forma se pou\u017E\u00EDv\u00E1 v teorii obvod\u016F. Ka\u017Ed\u00E1 konjunkce liter\u00E1l\u016F a tak\u00E9 ka\u017Ed\u00E1 disjunkce liter\u00E1l\u016F je KNF, proto\u017Ee je m\u016F\u017Eeme pova\u017Eovat za konjunkci klauzul\u00ED s jedn\u00EDm liter\u00E1lem, resp. za disjunkci jedn\u00E9 klauzule.Podobn\u011B jako vdisjunktivn\u00ED norm\u00E1ln\u00ED form\u011B (DNF), jedin\u00E9 logick\u00E9 spojky v KNF jsou logick\u00E1 spojka a, nebo a negace. Negace m\u016F\u017Ee b\u00FDt pouze sou\u010D\u00E1st\u00ED liter\u00E1lu, tzn. \u017Ee negovat lze pouze v\u00FDrokovou prom\u011Bnnou. Plat\u00ED, \u017Ee pro ka\u017Edou formuli A lze sestrojit ekvivalentn\u00ED formule K a D (tedy A \u2194 K a A \u2194 D), kde K je v KNF a D je v DNF. Toto tvrzen\u00ED lze dok\u00E1zat indukc\u00ED podle slo\u017Eitosti formule u\u017Eit\u00EDm De Morganov\u00FDch z\u00E1kon\u016F a distributivity."@cs . . . . . . . . . . "73342"^^ . . "Koniunkcyjna posta\u0107 normalna (ang. conjunctive normal form, CNF) danej formu\u0142y logicznej to r\u00F3wnowa\u017Cna jej formu\u0142a zapisana w postaci koniunkcji klauzul. Na przyk\u0142ad koniunkcyjn\u0105 postaci\u0105 normaln\u0105 wyra\u017Cenia jest Ka\u017Cde wyra\u017Cenie logiczne ma koniunkcyjn\u0105 posta\u0107 normaln\u0105. Przyk\u0142ady przekszta\u0142ce\u0144:"@pl . . . . . "Koniunkcyjna posta\u0107 normalna"@pl . "\u041A\u043E\u043D\u044A\u044E\u043D\u043A\u0442\u0438\u0301\u0432\u043D\u0430\u044F \u043D\u043E\u0440\u043C\u0430\u0301\u043B\u044C\u043D\u0430\u044F \u0444\u043E\u0301\u0440\u043C\u0430 (\u041A\u041D\u0424) \u0432 \u0431\u0443\u043B\u0435\u0432\u043E\u0439 \u043B\u043E\u0433\u0438\u043A\u0435 \u2014 \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430\u044F \u0444\u043E\u0440\u043C\u0430, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0431\u0443\u043B\u0435\u0432\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0438\u043C\u0435\u0435\u0442 \u0432\u0438\u0434 \u043A\u043E\u043D\u044A\u044E\u043D\u043A\u0446\u0438\u0438 \u0434\u0438\u0437\u044A\u044E\u043D\u043A\u0446\u0438\u0439 \u043B\u0438\u0442\u0435\u0440\u0430\u043B\u043E\u0432. \u041A\u043E\u043D\u044A\u044E\u043D\u043A\u0442\u0438\u0432\u043D\u0430\u044F \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430\u044F \u0444\u043E\u0440\u043C\u0430 \u0443\u0434\u043E\u0431\u043D\u0430 \u0434\u043B\u044F \u0430\u0432\u0442\u043E\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u0430 \u0442\u0435\u043E\u0440\u0435\u043C. \u041B\u044E\u0431\u0430\u044F \u0431\u0443\u043B\u0435\u0432\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u043F\u0440\u0438\u0432\u0435\u0434\u0435\u043D\u0430 \u043A \u041A\u041D\u0424. \u0414\u043B\u044F \u044D\u0442\u043E\u0433\u043E \u043C\u043E\u0436\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u0442\u044C: \u0437\u0430\u043A\u043E\u043D \u0434\u0432\u043E\u0439\u043D\u043E\u0433\u043E \u043E\u0442\u0440\u0438\u0446\u0430\u043D\u0438\u044F, \u0437\u0430\u043A\u043E\u043D \u0434\u0435 \u041C\u043E\u0440\u0433\u0430\u043D\u0430, \u0434\u0438\u0441\u0442\u0440\u0438\u0431\u0443\u0442\u0438\u0432\u043D\u043E\u0441\u0442\u044C."@ru . "\u9023\u8A00\u6A19\u6E96\u5F62\uFF08\u308C\u3093\u3052\u3093\u3072\u3087\u3046\u3058\u3085\u3093\u3051\u3044\u3001\u82F1: Conjunctive normal form, CNF\uFF09\u306F\u3001\u6570\u7406\u8AD6\u7406\u5B66\u306B\u304A\u3044\u3066\u30D6\u30FC\u30EB\u8AD6\u7406\u306B\u304A\u3051\u308B\u8AD6\u7406\u5F0F\u306E\u6A19\u6E96\u5316\uFF08\u6B63\u898F\u5316\uFF09\u306E\u4E00\u7A2E\u3067\u3042\u308A\u3001\u9078\u8A00\u7BC0\u306E\u9023\u8A00\u306E\u5F62\u5F0F\u3067\u8AD6\u7406\u5F0F\u3092\u8868\u3059\u3002\u4E57\u6CD5\u6A19\u6E96\u5F62\u3001\u4E3B\u4E57\u6CD5\u6A19\u6E96\u5F62\u3001\u548C\u7A4D\u6A19\u6E96\u5F62\u3068\u3082\u547C\u3076\u3002\u6B63\u898F\u5F62\u3068\u3057\u3066\u306F\u3001\u81EA\u52D5\u5B9A\u7406\u8A3C\u660E\u3067\u5229\u7528\u3055\u308C\u3066\u3044\u308B\u3002"@ja . "Forma normale congiuntiva"@it . "\u9023\u8A00\u6A19\u6E96\u5F62\uFF08\u308C\u3093\u3052\u3093\u3072\u3087\u3046\u3058\u3085\u3093\u3051\u3044\u3001\u82F1: Conjunctive normal form, CNF\uFF09\u306F\u3001\u6570\u7406\u8AD6\u7406\u5B66\u306B\u304A\u3044\u3066\u30D6\u30FC\u30EB\u8AD6\u7406\u306B\u304A\u3051\u308B\u8AD6\u7406\u5F0F\u306E\u6A19\u6E96\u5316\uFF08\u6B63\u898F\u5316\uFF09\u306E\u4E00\u7A2E\u3067\u3042\u308A\u3001\u9078\u8A00\u7BC0\u306E\u9023\u8A00\u306E\u5F62\u5F0F\u3067\u8AD6\u7406\u5F0F\u3092\u8868\u3059\u3002\u4E57\u6CD5\u6A19\u6E96\u5F62\u3001\u4E3B\u4E57\u6CD5\u6A19\u6E96\u5F62\u3001\u548C\u7A4D\u6A19\u6E96\u5F62\u3068\u3082\u547C\u3076\u3002\u6B63\u898F\u5F62\u3068\u3057\u3066\u306F\u3001\u81EA\u52D5\u5B9A\u7406\u8A3C\u660E\u3067\u5229\u7528\u3055\u308C\u3066\u3044\u308B\u3002"@ja . . . . "In de logica is een formule in conjunctieve normaalvorm (Eng. conjunctive normal form, CNF, ook wel afgekort als CNV) als die bestaat uit een conjunctie van disjuncties met literalen (ook een conjunctie van clausules genoemd). In een conjunctieve normaalvorm komen alleen de booleaanse operatoren 'en', 'of' en negatie voor, waarbij de negatie alleen als onderdeel van een literaal kan voorkomen. Er bestaat ook een disjunctieve normaalvorm, een disjunctie van conjuncties."@nl . "p/c025090"@en . . . "Na l\u00F3gica booleana, uma f\u00F3rmula est\u00E1 na forma normal conjuntiva (FNC) se \u00E9 uma conjun\u00E7\u00E3o de cl\u00E1usulas, onde uma cl\u00E1usula \u00E9 uma disjun\u00E7\u00E3o de literais. Sendo uma forma normal, a FNC \u00E9 \u00FAtil em . Ela \u00E9 similar \u00E0 usada na teoria dos circuitos. Toda conjun\u00E7\u00E3o de literais e toda disjun\u00E7\u00E3o de literais est\u00E3o na FNC, j\u00E1 que elas podem ser vistas como conjun\u00E7\u00F5es de cl\u00E1usulas de um literal e conjun\u00E7\u00F5es de uma s\u00F3 cl\u00E1usula, respectivamente. Assim como na forma normal disjuntiva (FND), os \u00FAnicos conectivos proposicionais que uma f\u00F3rmula na FNC pode conter s\u00E3o os operadores e, ou e n\u00E3o. O operador n\u00E3o pode ser usado apenas como parte de um literal, e portanto ele pode aparecer apenas na frente de . Por exemplo, todas as f\u00F3rmulas seguintes est\u00E3o na FNC: : Por\u00E9m, as seguintes f\u00F3rmulas n\u00E3o est\u00E3o: As tr\u00EAs f\u00F3rmulas acima s\u00E3o equivalentes respectivamente \u00E0s tr\u00EAs f\u00F3rmulas seguintes que est\u00E3o na forma normal conjuntiva: Toda f\u00F3rmula proposicional pode ser convertida para uma f\u00F3rmula equivalente que est\u00E1 na FNC.Essa transforma\u00E7\u00E3o \u00E9 baseada em regras sobre : Lei da Dupla Nega\u00E7\u00E3o, Leis de De Morgan, e a Distributividade. Uma vez que todas as f\u00F3rmulas l\u00F3gicas cl\u00E1ssicas podem ser convertidas em f\u00F3rmulas equivalentes na forma normal conjuntiva, muitas demonstra\u00E7\u00F5es s\u00E3o baseadas na suposi\u00E7\u00E3o de que todas as f\u00F3rmulas est\u00E3o na FNC. Contudo, em alguns casos, essa convers\u00E3o para FNC pode levar a uma explos\u00E3o exponencial da f\u00F3rmula. Por exemplo, traduzindo a seguinte f\u00F3rmula que n\u00E3o est\u00E1 na FNC para FNC, obtemos uma f\u00F3rmula com cl\u00E1usulas: A seguinte f\u00F3rmula \u00E9 uma gram\u00E1tica formal para FNC: 1. \u2192 \u22282. \u2192 \u22273. \u2192 \u00AC4. \u2192 5. \u2192 6. \u2192 7. \u21928. \u2192 9. \u2192 Onde \u00E9 qualquer vari\u00E1vel. Existem transforma\u00E7\u00F5es das f\u00F3rmulas na FNC que preservam a satisfatibilidade ao inv\u00E9s da equival\u00EAncia e n\u00E3o produzem um aumento exponencial do tamanho. Tais transforma\u00E7\u00F5es aumentam o tamanho da f\u00F3rmula apenas por um fator linear, mas introduzem novas vari\u00E1veis. A forma normal conjuntiva pode ser levada adiante de modo a produzir a forma normal clausal de uma f\u00F3rmula l\u00F3gica, a qual \u00E9 usada para se efetuar resolu\u00E7\u00E3o de primeira ordem. Um importante conjunto de problemas em complexidade computacional envolve encontrar atribui\u00E7\u00F5es para as vari\u00E1veis de uma f\u00F3rmula booleana expressa na Forma Normal Conjuntiva, tais que a f\u00F3rmula seja satisfeita. O problema k-SAT \u00E9 o problema de encontrar uma atribui\u00E7\u00E3o que satisfa\u00E7a para uma f\u00F3rmula booleana expressa na FNC, tal que cada disjun\u00E7\u00E3o contenha no m\u00E1ximo k vari\u00E1veis. 3-SAT \u00E9 NP-completo (assim como qualquer outro problema k-SAT com k>2), enquanto pode ser resolvido em ."@pt . . "\u041A\u043E\u043D\u044A\u044E\u043D\u043A\u0442\u0438\u0301\u0432\u043D\u0430\u044F \u043D\u043E\u0440\u043C\u0430\u0301\u043B\u044C\u043D\u0430\u044F \u0444\u043E\u0301\u0440\u043C\u0430 (\u041A\u041D\u0424) \u0432 \u0431\u0443\u043B\u0435\u0432\u043E\u0439 \u043B\u043E\u0433\u0438\u043A\u0435 \u2014 \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430\u044F \u0444\u043E\u0440\u043C\u0430, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0431\u0443\u043B\u0435\u0432\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0438\u043C\u0435\u0435\u0442 \u0432\u0438\u0434 \u043A\u043E\u043D\u044A\u044E\u043D\u043A\u0446\u0438\u0438 \u0434\u0438\u0437\u044A\u044E\u043D\u043A\u0446\u0438\u0439 \u043B\u0438\u0442\u0435\u0440\u0430\u043B\u043E\u0432. \u041A\u043E\u043D\u044A\u044E\u043D\u043A\u0442\u0438\u0432\u043D\u0430\u044F \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430\u044F \u0444\u043E\u0440\u043C\u0430 \u0443\u0434\u043E\u0431\u043D\u0430 \u0434\u043B\u044F \u0430\u0432\u0442\u043E\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0433\u043E \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u0430 \u0442\u0435\u043E\u0440\u0435\u043C. \u041B\u044E\u0431\u0430\u044F \u0431\u0443\u043B\u0435\u0432\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u043F\u0440\u0438\u0432\u0435\u0434\u0435\u043D\u0430 \u043A \u041A\u041D\u0424. \u0414\u043B\u044F \u044D\u0442\u043E\u0433\u043E \u043C\u043E\u0436\u043D\u043E \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u0442\u044C: \u0437\u0430\u043A\u043E\u043D \u0434\u0432\u043E\u0439\u043D\u043E\u0433\u043E \u043E\u0442\u0440\u0438\u0446\u0430\u043D\u0438\u044F, \u0437\u0430\u043A\u043E\u043D \u0434\u0435 \u041C\u043E\u0440\u0433\u0430\u043D\u0430, \u0434\u0438\u0441\u0442\u0440\u0438\u0431\u0443\u0442\u0438\u0432\u043D\u043E\u0441\u0442\u044C."@ru . . "En logique bool\u00E9enne et en calcul des propositions, une formule en forme normale conjonctive ou FNC (en anglais, Conjunctive Normal Form, Clausal Normal Form ou CNF) est une conjonction de clauses, o\u00F9 une clause est une disjonction de litt\u00E9raux. Les formules en FNC sont utilis\u00E9es dans le cadre de la d\u00E9monstration automatique de th\u00E9or\u00E8mes ou encore dans la r\u00E9solution du probl\u00E8me SAT (en particulier dans l'algorithme DPLL)."@fr . "Als konjunktive Normalform (kurz KNF, englisch CNF f\u00FCr conjunctive normal form) wird in der Aussagenlogik eine bestimmte Form von Formeln bezeichnet."@de . . . . "Forma normal conjuntiva"@ca . "In de logica is een formule in conjunctieve normaalvorm (Eng. conjunctive normal form, CNF, ook wel afgekort als CNV) als die bestaat uit een conjunctie van disjuncties met literalen (ook een conjunctie van clausules genoemd). In een conjunctieve normaalvorm komen alleen de booleaanse operatoren 'en', 'of' en negatie voor, waarbij de negatie alleen als onderdeel van een literaal kan voorkomen. Er bestaat ook een disjunctieve normaalvorm, een disjunctie van conjuncties. Elke formule kan omgezet worden naar een equivalente formule in conjunctieve normaalvorm met behulp van equivalentieregels (zoals de wetten van De Morgan en distributiviteit) die de formule omschrijven naar een logisch equivalente vorm in CNF."@nl . "Conjunctieve normaalvorm"@nl . . . . "\uBD88 \uB300\uC218\uC5D0\uC11C \uB17C\uB9AC\uACF1 \uD45C\uC900\uD615(conjunctive normal form)\uC740 \uC758 \uB17C\uB9AC\uACF1\uC73C\uB85C \uB098\uD0C0\uB0B8 \uB17C\uB9AC\uC2DD\uC744 \uB9D0\uD55C\uB2E4. \uC5EC\uAE30\uC11C \uC808\uC740 \uC758 \uB17C\uB9AC\uD569\uC73C\uB85C \uC774\uB8E8\uC5B4\uC9C4\uB2E4. \uB17C\uB9AC\uACF1 \uD45C\uC900\uD615\uC758 \uC601\uBB38 \uD45C\uAE30\uB97C \uC904\uC5EC\uC11C CNF\uB77C\uACE0\uB3C4 \uD55C\uB2E4. CNF\uC640 \uBC18\uB300\uB85C \uB9AC\uD130\uB7F4\uC758 \uB17C\uB9AC\uACF1\uC73C\uB85C \uC774\uB8E8\uC5B4\uC9C4 \uC808\uB4E4\uC744 \uB17C\uB9AC\uD569\uC73C\uB85C \uC5F0\uACB0\uD560 \uC218\uB3C4 \uC788\uB2E4. \uC774\uB97C \uC774\uB77C\uACE0 \uD55C\uB2E4. \uBAA8\uB4E0 \uBA85\uC81C \uB17C\uB9AC\uC2DD\uC740 \uB3D9\uB4F1\uD55C CNF\uB85C \uBCC0\uD658\uB420 \uC218 \uC788\uB2E4. \uC774 \uBCC0\uD658\uC740 \uC774\uC911\uBD80\uC815 \uBC95\uCE59, \uB4DC\uBAA8\uB974\uAC04 \uBC95\uCE59, \uBD84\uBC30 \uBC95\uCE59 \uB4F1\uC744 \uC368\uC11C \uC774\uB8E8\uC5B4\uC9C4\uB2E4. \uB9AC\uD130\uB7F4\uC758 \uAC1C\uC218\uAC00 3\uAC1C \uC774\uD558\uB85C \uC81C\uD55C\uB41C CNF\uB97C 3-CNF\uB77C\uACE0 \uD558\uBA70 \uACC4\uC0B0 \uC774\uB860\uC5D0\uC11C \uC911\uC694\uD558\uAC8C \uB2E4\uB8E8\uC5B4\uC9C4\uB2E4. \uB2E4\uB978 \uAC1C\uC218\uB85C \uC81C\uD55C\uD560 \uB54C\uB3C4 \uB9C8\uCC2C\uAC00\uC9C0\uB85C \uC815\uC758\uD560 \uC218 \uC788\uC73C\uB098 2-CNF, 3-CNF \uC774\uC678\uC5D0\uB294 \uC911\uC694\uD558\uAC8C \uB2E4\uB8E8\uC9C0 \uC54A\uB294\uB2E4."@ko . "\uB17C\uB9AC\uACF1 \uD45C\uC900\uD615"@ko . "\u041A\u043E\u043D'\u044E\u043D\u043A\u0442\u0438\u0301\u0432\u043D\u0430 \u043D\u043E\u0440\u043C\u0430\u0301\u043B\u044C\u043D\u0430 \u0444\u043E\u0301\u0440\u043C\u0430 (\u041A\u041D\u0424) \u0432 \u0431\u0443\u043B\u0435\u0432\u0456\u0439 \u043B\u043E\u0433\u0456\u0446\u0456 - \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430 \u0444\u043E\u0440\u043C\u0430 \u0432 \u044F\u043A\u0456\u0439 \u0431\u0443\u043B\u0435\u0432\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u043C\u0430\u0454 \u0432\u0438\u0434 \u043A\u043E\u043D'\u044E\u043D\u043A\u0446\u0456\u0457 \u0434\u0435\u043A\u0456\u043B\u044C\u043A\u043E\u0445 \u0434\u0438\u0437'\u044E\u043D\u043A\u0442\u0456\u0432 (\u0434\u0435 \u0434\u0438\u0437'\u044E\u043D\u043A\u0442\u0430\u043C\u0438 \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C\u0441\u044F \u0434\u0438\u0437'\u044E\u043D\u043A\u0446\u0456\u0457 \u0434\u0435\u043A\u0456\u043B\u044C\u043A\u043E\u0445 \u043F\u0440\u043E\u043F\u043E\u0437\u0438\u0446\u0456\u0439\u043D\u0438\u0445 \u0441\u0438\u043C\u0432\u043E\u043B\u0456\u0432 \u0430\u0431\u043E \u0457\u0445 \u0437\u0430\u043F\u0435\u0440\u0435\u0447\u0435\u043D\u044C). \u041A\u043E\u043D'\u044E\u043D\u043A\u0442\u0438\u0432\u043D\u0430 \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0430 \u0444\u043E\u0440\u043C\u0430 \u0448\u0438\u0440\u043E\u043A\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0432 \u0430\u0432\u0442\u043E\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u0456 \u0442\u0435\u043E\u0440\u0435\u043C, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u0432\u043E\u043D\u0430 \u0454 \u043E\u0441\u043D\u043E\u0432\u043E\u044E \u0434\u043B\u044F \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u0430\u043D\u043D\u044F \u043F\u0440\u0430\u0432\u0438\u043B\u0430 \u0440\u0435\u0437\u043E\u043B\u044E\u0446\u0456\u0457."@uk . . . . . "En logique bool\u00E9enne et en calcul des propositions, une formule en forme normale conjonctive ou FNC (en anglais, Conjunctive Normal Form, Clausal Normal Form ou CNF) est une conjonction de clauses, o\u00F9 une clause est une disjonction de litt\u00E9raux. Les formules en FNC sont utilis\u00E9es dans le cadre de la d\u00E9monstration automatique de th\u00E9or\u00E8mes ou encore dans la r\u00E9solution du probl\u00E8me SAT (en particulier dans l'algorithme DPLL)."@fr . "Nella logica booleana, una formula \u00E8 in forma normale congiuntiva o congiunta (FNC), indicata anche come CNF (acronimo di Conjunctive Normal Form) se \u00E8 una congiunzione di clausole, dove le clausole sono una disgiunzione di letterali. Una formula in CNF ha quindi la seguente struttura: : Numero di clausole. : Numero di letterali della clausola i-esima. : \u00C8 il k-esimo letterale della i-esima clausola. Un letterale pu\u00F2 essere una variabile booleana (cio\u00E8 che pu\u00F2 valere solo 0 o 1, vero o falso) o la negazione di una variabile. Una funzione booleana \u00E8 una funzione che ha in ingresso diversi valori booleani (cio\u00E8 vero/falso oppure 1/0) e come risultato ha un valore booleano. Per ogni funzione booleana, esiste una formula in forma normale congiuntiva che produce come risultato gli stessi valori."@it . "1097076255"^^ . "Vev\u00FDrokov\u00E9 logice je formule v konjunktivn\u00ED norm\u00E1ln\u00ED form\u011B (KNF nebo CNF z anglick\u00E9ho conjunctive normal form), pokud je ve tvaru konjunkc\u00ED , kde klauzuli definujeme jako disjunkci (a je-li v\u00FDrokov\u00E1 prom\u011Bnn\u00E1, tak j\u00ED ur\u010Den\u00E9 liter\u00E1ly jsou pr\u00E1v\u011B a ). Jako norm\u00E1ln\u00ED forma se pou\u017E\u00EDv\u00E1 v . Podobn\u00E1 kanonick\u00E1 forma se pou\u017E\u00EDv\u00E1 v teorii obvod\u016F. Plat\u00ED, \u017Ee pro ka\u017Edou formuli A lze sestrojit ekvivalentn\u00ED formule K a D (tedy A \u2194 K a A \u2194 D), kde K je v KNF a D je v DNF. Toto tvrzen\u00ED lze dok\u00E1zat indukc\u00ED podle slo\u017Eitosti formule u\u017Eit\u00EDm De Morganov\u00FDch z\u00E1kon\u016F a distributivity."@cs . . . . . "\u5728\u5E03\u5C14\u903B\u8F91\u4E2D\uFF0C\u5982\u679C\u4E00\u4E2A\u516C\u5F0F\u662F\u5B50\u53E5\u7684\u5408\u53D6\uFF0C\u90A3\u4E48\u5B83\u662F\u5408\u53D6\u8303\u5F0F(CNF)\u7684\u3002\u4F5C\u4E3A\u89C4\u8303\u5F62\u5F0F\uFF0C\u5B83\u5728\u81EA\u52A8\u5B9A\u7406\u8BC1\u660E\u4E2D\u6709\u7528\u3002\u5B83\u7C7B\u4F3C\u4E8E\u5728\u7535\u8DEF\u7406\u8BBA\u4E2D\u7684\u3002 \u6240\u6709\u7684\u6587\u5B57\u7684\u5408\u53D6\u548C\u6240\u6709\u7684\u6587\u5B57\u7684\u6790\u53D6\u662F CNF \u7684\uFF0C\u56E0\u4E3A\u53EF\u4EE5\u88AB\u5206\u522B\u770B\u4F5C\u4E00\u4E2A\u6587\u5B57\u7684\u5B50\u53E5\u7684\u5408\u53D6\u548C\u6790\u53D6\u3002\u548C\u6790\u53D6\u8303\u5F0F(DNF)\u4E2D\u4E00\u6837\uFF0C\u5728 CNF \u516C\u5F0F\u4E2D\u53EF\u4EE5\u5305\u542B\u7684\u547D\u9898\u8FDE\u7ED3\u8BCD\u662F\u4E0E\u3001\u6216\u548C\u975E\u3002\u975E\u7B97\u5B50\u53EA\u80FD\u7528\u505A\u6587\u5B57\u7684\u4E00\u90E8\u5206\uFF0C\u8FD9\u610F\u5473\u7740\u5B83\u53EA\u80FD\u5728\u547D\u9898\u53D8\u91CF\u524D\u51FA\u73B0\u3002 \u4F8B\u5982\uFF0C\u4E0B\u5217\u6240\u6709\u516C\u5F0F\u90FD\u662F CNF: \u800C\u4E0B\u5217\u4E0D\u662F: \u4E0A\u8FF0\u4E09\u4E2A\u516C\u5F0F\u5206\u522B\u7B49\u4EF7\u4E8E\u5408\u53D6\u8303\u5F0F\u7684\u4E0B\u5217\u4E09\u4E2A\u516C\u5F0F: \u6240\u6709\u547D\u9898\u516C\u5F0F\u90FD\u53EF\u4EE5\u8F6C\u6362\u6210 CNF \u7684\u7B49\u4EF7\u516C\u5F0F\u3002\u8FD9\u79CD\u53D8\u6362\u57FA\u4E8E\u4E86\u5173\u4E8E\u903B\u8F91\u7B49\u4EF7\u7684\u89C4\u5219: \u53CC\u91CD\u5426\u5B9A\u5F8B\u3001\u5FB7\u00B7\u6469\u6839\u5B9A\u5F8B\u548C\u5206\u914D\u5F8B\u3002 \u56E0\u4E3A\u6240\u6709\u903B\u8F91\u516C\u5F0F\u90FD\u53EF\u4EE5\u8F6C\u6362\u6210\u5408\u53D6\u8303\u5F0F\u7684\u7B49\u4EF7\u516C\u5F0F\uFF0C\u8BC1\u660E\u7ECF\u5E38\u57FA\u4E8E\u6240\u6709\u516C\u5F0F\u90FD\u662F CNF \u7684\u5047\u5B9A\u3002\u4F46\u662F\u5728\u67D0\u4E9B\u60C5\u51B5\u4E0B\uFF0C\u8FD9\u79CD\u5230 CNF \u7684\u8F6C\u6362\u53EF\u80FD\u5BFC\u81F4\u516C\u5F0F\u7684\u6307\u6570\u6027\u7206\u6DA8\u3002\u4F8B\u5982\uFF0C\u628A\u4E0B\u8FF0\u975E-CNF \u516C\u5F0F\u8F6C\u6362\u6210 CNF \u751F\u6210\u6709 \u4E2A\u5B50\u53E5\u7684\u516C\u5F0F:"@zh . . . "Koniunkcyjna posta\u0107 normalna (ang. conjunctive normal form, CNF) danej formu\u0142y logicznej to r\u00F3wnowa\u017Cna jej formu\u0142a zapisana w postaci koniunkcji klauzul. Na przyk\u0142ad koniunkcyjn\u0105 postaci\u0105 normaln\u0105 wyra\u017Cenia jest Ka\u017Cde wyra\u017Cenie logiczne ma koniunkcyjn\u0105 posta\u0107 normaln\u0105. Przyk\u0142ady przekszta\u0142ce\u0144:"@pl . . . . "20930"^^ . "Forma normal conjuntiva"@es . . "In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. As a canonical normal form, it is useful in automated theorem proving and circuit theory. In automated theorem proving, the notion \"clausal normal form\" is often used in a narrower sense, meaning a particular representation of a CNF formula as a set of sets of literals."@en . . "In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. As a canonical normal form, it is useful in automated theorem proving and circuit theory. All conjunctions of literals and all disjunctions of literals are in CNF, as they can be seen as conjunctions of one-literal clauses and conjunctions of a single clause, respectively. As in the disjunctive normal form (DNF), the only propositional connectives a formula in CNF can contain are and, or, and not. The not operator can only be used as part of a literal, which means that it can only precede a propositional variable or a predicate symbol. In automated theorem proving, the notion \"clausal normal form\" is often used in a narrower sense, meaning a particular representation of a CNF formula as a set of sets of literals."@en . . "Konjunktive Normalform"@de .