. . . . . "3720"^^ . "\u8AD6\u7406\u5F0F\u306E\u30A8\u30EB\u30D6\u30E9\u30F3\u5316\uFF08\u82F1: Herbrandization\uFF09\u3068\u306F\u3001\u8AD6\u7406\u5F0F\u306E\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u306E\u53CC\u5BFE\u3068\u306A\u308B\u69CB\u6210\u3067\u3042\u308B\u3002\u30B8\u30E3\u30C3\u30AF\u30FB\u30A8\u30EB\u30D6\u30E9\u30F3\u306B\u56E0\u3080\u3002\u30C8\u30A2\u30EB\u30D5\u30FB\u30B9\u30B3\u30FC\u30EC\u30E0\u306F\u3001\u30EC\u30FC\u30F4\u30A7\u30F3\u30CF\u30A4\u30E0\u2013\u30B9\u30B3\u30FC\u30EC\u30E0\u306E\u5B9A\u7406\uFF08Skolem 1920\uFF09\u306E\u8A3C\u660E\u306E\u4E00\u90E8\u3068\u3057\u3066\u3001\u51A0\u982D\u6A19\u6E96\u5F62\u306E\u8AD6\u7406\u5F0F\u306E\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u3092\u8003\u3048\u3066\u3044\u305F\u3002\u30A8\u30EB\u30D6\u30E9\u30F3\u306F\u3001\u30A8\u30EB\u30D6\u30E9\u30F3\u306E\u5B9A\u7406\uFF08Herbrand 1930\uFF09\u3092\u8A3C\u660E\u3059\u308B\u305F\u3081\u3001\u305D\u306E\u53CC\u5BFE\u6982\u5FF5\u3067\u3042\u308B\u30A8\u30EB\u30D6\u30E9\u30F3\u5316\uFF08\u51A0\u982D\u6A19\u6E96\u5F62\u4EE5\u5916\u306E\u8AD6\u7406\u5F0F\u306B\u3082\u9069\u7528\u3067\u304D\u308B\u3088\u3046\u4E00\u822C\u5316\u3055\u308C\u305F\u3082\u306E\uFF09\u3092\u7528\u3044\u305F\u3002 \u7D50\u679C\u306E\u8AD6\u7406\u5F0F\u306F\u5143\u3005\u306E\u8AD6\u7406\u5F0F\u3068\u8AD6\u7406\u7684\u540C\u5024\u3067\u3042\u308B\u5FC5\u8981\u306F\u306A\u3044\u3002\u5145\u8DB3\u53EF\u80FD\u6027\u3092\u4FDD\u3064\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u3068\u540C\u69D8\u3001\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u306E\u53CC\u5BFE\u3067\u3042\u308B\u30A8\u30EB\u30D6\u30E9\u30F3\u5316\u306F\u8AD6\u7406\u7684\u59A5\u5F53\u6027\u3092\u4FDD\u3064\uFF1A\u7D50\u679C\u306E\u8AD6\u7406\u5F0F\u304C\u59A5\u5F53\u3067\u3042\u308B\u306E\u306F\u3001\u5143\u3005\u306E\u8AD6\u7406\u5F0F\u304C\u59A5\u5F53\u3067\u3042\u308B\u3068\u304D\u3001\u304B\u3064\u305D\u306E\u3068\u304D\u306B\u9650\u308B\u3002"@ja . "The Herbrandization of a logical formula (named after Jacques Herbrand) is a construction that is dual to the Skolemization of a formula. Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the L\u00F6wenheim\u2013Skolem theorem (Skolem 1920). Herbrand worked with this dual notion of Herbrandization, generalized to apply to non-prenex formulas as well, in order to prove Herbrand's theorem (Herbrand 1930). The resulting formula is not necessarily equivalent to the original one. As with Skolemization, which only preserves satisfiability, Herbrandization being Skolemization's dual preserves validity: the resulting formula is valid if and only if the original one is."@en . . "1070544322"^^ . . . . . . "Herbrandization"@en . . . "A Herbrandiza\u00E7\u00E3o de uma f\u00F3rmula l\u00F3gica (denomina\u00E7\u00E3o em homenagem a Jacques Herbrand) \u00E9 um constru\u00E7\u00E3o que \u00E9 dual \u00E0 Skolemiza\u00E7\u00E3o de uma f\u00F3rmula. Thoralf Skolem tinha considerado a Skolemiza\u00E7\u00E3o de f\u00F3rmulas na Forma normal prenex como parte da prova do Teorema de L\u00F6wenheim\u2013Skolem (Skolem 1920). Herbrand trabalhou com essa no\u00E7\u00E3o dual de Herbrandiza\u00E7\u00E3o, generalizada para se aplicar a f\u00F3rmulas n\u00E3o-prenex tamb\u00E9m, com o objetivo de provar o Teorema de Herbrand (Herbrand 1930). A f\u00F3rmula resultante n\u00E3o \u00E9 necessariamente equivalente \u00E0 original. Assim como acontece na Skolemiza\u00E7\u00E3o, que somente preserva a satisfatibilidade, a Herbrandiza\u00E7\u00E3o sendo uma dual da Skolemiza\u00E7\u00E3o, preserva a validade: a f\u00F3rmula resultante \u00E9 v\u00E1lida se e somente se a original for. Seja uma f\u00F3rmula na linguagem da L\u00F3gica de primeira ordem. Podemos assumir que n\u00E3o cont\u00E9m nenhuma vari\u00E1vel que est\u00E1 ligada a duas ocorr\u00EAncias de quantificadores diferentes, e que nenhuma vari\u00E1vel ocorre livre e ligada. (Ou seja, pode ser reescrita para assegurar essas condi\u00E7\u00F5es, de modo que o resultado \u00E9 uma f\u00F3rmula equivalente). A Herbrandiza\u00E7\u00E3o de \u00E9 obtida da seguinte maneira: \n* Primeiro, substitua qualquer vari\u00E1vel livre em por s\u00EDmbolos de constante; \n* Depois, remova todos os quantificadores nas vari\u00E1veis que (1) sejam quantificadas universalmente e que estejam dentro do escopo de uma quantidade par de s\u00EDmbolos de nega\u00E7\u00E3o, ou (2) que sejam quantificadas existencialmente, e com estejam dentro do escopo de uma quantidade impar de s\u00EDmbolos de nega\u00E7\u00E3o; \n* Finalmente, substitua cada vari\u00E1vel por um s\u00EDmbolo de fun\u00E7\u00E3o, , onde s\u00E3o as vari\u00E1veis que continuam quantificadas, e cujos quantificadores dominam ."@pt . . "Herbrandiza\u00E7\u00E3o"@pt . . . "\u30A8\u30EB\u30D6\u30E9\u30F3\u5316"@ja . "5821699"^^ . . . . "A Herbrandiza\u00E7\u00E3o de uma f\u00F3rmula l\u00F3gica (denomina\u00E7\u00E3o em homenagem a Jacques Herbrand) \u00E9 um constru\u00E7\u00E3o que \u00E9 dual \u00E0 Skolemiza\u00E7\u00E3o de uma f\u00F3rmula. Thoralf Skolem tinha considerado a Skolemiza\u00E7\u00E3o de f\u00F3rmulas na Forma normal prenex como parte da prova do Teorema de L\u00F6wenheim\u2013Skolem (Skolem 1920). Herbrand trabalhou com essa no\u00E7\u00E3o dual de Herbrandiza\u00E7\u00E3o, generalizada para se aplicar a f\u00F3rmulas n\u00E3o-prenex tamb\u00E9m, com o objetivo de provar o Teorema de Herbrand (Herbrand 1930). A Herbrandiza\u00E7\u00E3o de \u00E9 obtida da seguinte maneira:"@pt . "The Herbrandization of a logical formula (named after Jacques Herbrand) is a construction that is dual to the Skolemization of a formula. Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the L\u00F6wenheim\u2013Skolem theorem (Skolem 1920). Herbrand worked with this dual notion of Herbrandization, generalized to apply to non-prenex formulas as well, in order to prove Herbrand's theorem (Herbrand 1930)."@en . . . . . . "\u8AD6\u7406\u5F0F\u306E\u30A8\u30EB\u30D6\u30E9\u30F3\u5316\uFF08\u82F1: Herbrandization\uFF09\u3068\u306F\u3001\u8AD6\u7406\u5F0F\u306E\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u306E\u53CC\u5BFE\u3068\u306A\u308B\u69CB\u6210\u3067\u3042\u308B\u3002\u30B8\u30E3\u30C3\u30AF\u30FB\u30A8\u30EB\u30D6\u30E9\u30F3\u306B\u56E0\u3080\u3002\u30C8\u30A2\u30EB\u30D5\u30FB\u30B9\u30B3\u30FC\u30EC\u30E0\u306F\u3001\u30EC\u30FC\u30F4\u30A7\u30F3\u30CF\u30A4\u30E0\u2013\u30B9\u30B3\u30FC\u30EC\u30E0\u306E\u5B9A\u7406\uFF08Skolem 1920\uFF09\u306E\u8A3C\u660E\u306E\u4E00\u90E8\u3068\u3057\u3066\u3001\u51A0\u982D\u6A19\u6E96\u5F62\u306E\u8AD6\u7406\u5F0F\u306E\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u3092\u8003\u3048\u3066\u3044\u305F\u3002\u30A8\u30EB\u30D6\u30E9\u30F3\u306F\u3001\u30A8\u30EB\u30D6\u30E9\u30F3\u306E\u5B9A\u7406\uFF08Herbrand 1930\uFF09\u3092\u8A3C\u660E\u3059\u308B\u305F\u3081\u3001\u305D\u306E\u53CC\u5BFE\u6982\u5FF5\u3067\u3042\u308B\u30A8\u30EB\u30D6\u30E9\u30F3\u5316\uFF08\u51A0\u982D\u6A19\u6E96\u5F62\u4EE5\u5916\u306E\u8AD6\u7406\u5F0F\u306B\u3082\u9069\u7528\u3067\u304D\u308B\u3088\u3046\u4E00\u822C\u5316\u3055\u308C\u305F\u3082\u306E\uFF09\u3092\u7528\u3044\u305F\u3002 \u7D50\u679C\u306E\u8AD6\u7406\u5F0F\u306F\u5143\u3005\u306E\u8AD6\u7406\u5F0F\u3068\u8AD6\u7406\u7684\u540C\u5024\u3067\u3042\u308B\u5FC5\u8981\u306F\u306A\u3044\u3002\u5145\u8DB3\u53EF\u80FD\u6027\u3092\u4FDD\u3064\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u3068\u540C\u69D8\u3001\u30B9\u30B3\u30FC\u30EC\u30E0\u5316\u306E\u53CC\u5BFE\u3067\u3042\u308B\u30A8\u30EB\u30D6\u30E9\u30F3\u5316\u306F\u8AD6\u7406\u7684\u59A5\u5F53\u6027\u3092\u4FDD\u3064\uFF1A\u7D50\u679C\u306E\u8AD6\u7406\u5F0F\u304C\u59A5\u5F53\u3067\u3042\u308B\u306E\u306F\u3001\u5143\u3005\u306E\u8AD6\u7406\u5F0F\u304C\u59A5\u5F53\u3067\u3042\u308B\u3068\u304D\u3001\u304B\u3064\u305D\u306E\u3068\u304D\u306B\u9650\u308B\u3002"@ja . .