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In logica matematica, nell'ambito della te … In logica matematica, nell'ambito della teoria della dimostrazione, un'estensione conservativa di una teoria logica T1 è una teoria T2 tale che:
* tutti i simboli di T1 sono presenti anche in T2
* ogni teorema di T1 è anche un teorema di T2
* ogni teorema di T2 esprimibile usando soltanto il linguaggio di T1 è un teorema di T1. Nella teoria dei modelli, T2 si dice un'estensione conservativa di T1 se ogni modello di T1 può essere esteso in un modello di T2. Tutte le estensioni conservative nel senso della teoria dei modelli lo sono anche nella definizione della teoria della dimostrazione.inizione della teoria della dimostrazione.
, 保守扩展是逻辑中的一个概念。一个知识库K'是K的扩展，如果K是K'的一个子集；K'是 … 保守扩展是逻辑中的一个概念。一个知识库K'是K的扩展，如果K是K'的一个子集；K'是K的保守扩展，如果对所有只用K中的名字构造的命题, K' 当且仅当 K。换句话说，保守扩展不会改变原有的知识库的结构。保守扩展在许多领域都有应用，如模块化本体和敏感知识的保护。 在逻辑和推导机制中，I和J分别是一个解释(Interpretation),如果J是I的保守扩展，必须满足以下条件:
* 1) 解释I作用在语言集合L中，解释J必须作用在语言集合L'中,并且L'包含L
* 2) 解释I的域(Domain)等于解释J的域
* 3) 对于任何在语言集合L中的元素e，I(e) = J(e) 那么我们说J是I的保守扩展。对于任何在语言集合L中的元素e，I(e) = J(e) 那么我们说J是I的保守扩展。
, En logique mathématique, une théorie logiq … En logique mathématique, une théorie logique T2 est une extension conservatrice (ou conservative) d'une théorie T1 si le langage de T2 étend le langage de T1, si chaque théorème de T1 est un théorème de T2 et si tout théorème de T2 qui est dans le langage de T1 est déjà un théorème de T1. Une extension propre est une extension non conservative. Informellement, cela veut dire que la nouvelle théorie peut éventuellement être plus commode pour prouver des théorèmes, mais qu’elle ne prouve pas de théorème nouveau concernant l'ancienne théorie. L'importance de cette notion réside dans le théorème suivant : si T2 est une extension conservatrice de T1, et si T1 est cohérente, alors T2 est également cohérente. Ainsi, les extensions conservatrices ne courent pas le risque d'introduire de nouvelles incohérences. Elles peuvent aussi être vues comme une méthode pour écrire et structurer des théories volumineuses : on commence avec une théorie T0 connue comme cohérente, puis on construit successivement des extensions conservatrices T1, T2, etc. Le démonstrateur automatique Isabelle adopte cette méthodologie en fournissant un langage pour les extensions conservatrices par définition. extensions conservatrices par définition.
, In mathematical logic, a conservative exte … In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory. Similarly, a non-conservative extension is a supertheory which is not conservative, and can prove more theorems than the original. More formally stated, a theory is a (proof theoretic) conservative extension of a theory if every theorem of is a theorem of , and any theorem of in the language of is already a theorem of . More generally, if is a set of formulas in the common language of and , then is -conservative over if every formula from provable in is also provable in . Note that a conservative extension of a consistent theory is consistent. If it were not, then by the principle of explosion, every formula in the language of would be a theorem of , so every formula in the language of would be a theorem of , so would not be consistent. Hence, conservative extensions do not bear the risk of introducing new inconsistencies. This can also be seen as a methodology for writing and structuring large theories: start with a theory, , that is known (or assumed) to be consistent, and successively build conservative extensions , , ... of it. Recently, conservative extensions have been used for defining a notion of module for ontologies: if an ontology is formalized as a logical theory, a subtheory is a module if the whole ontology is a conservative extension of the subtheory. An extension which is not conservative may be called a proper extension.ervative may be called a proper extension.
, 수리논리학에서 보존적 확장(保存的擴張, 영어: conservative extension)은 주어진 이론을 확장하되, 원래 이론의 언어로서 나타낼 수 있는 모든 명제의 증명 가능성 여부가 바뀌지 않게 하는 확장이다.
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保守扩展是逻辑中的一个概念。一个知识库K'是K的扩展，如果K是K'的一个子集；K'是 … 保守扩展是逻辑中的一个概念。一个知识库K'是K的扩展，如果K是K'的一个子集；K'是K的保守扩展，如果对所有只用K中的名字构造的命题, K' 当且仅当 K。换句话说，保守扩展不会改变原有的知识库的结构。保守扩展在许多领域都有应用，如模块化本体和敏感知识的保护。 在逻辑和推导机制中，I和J分别是一个解释(Interpretation),如果J是I的保守扩展，必须满足以下条件:
* 1) 解释I作用在语言集合L中，解释J必须作用在语言集合L'中,并且L'包含L
* 2) 解释I的域(Domain)等于解释J的域
* 3) 对于任何在语言集合L中的元素e，I(e) = J(e) 那么我们说J是I的保守扩展。对于任何在语言集合L中的元素e，I(e) = J(e) 那么我们说J是I的保守扩展。
, En logique mathématique, une théorie logiq … En logique mathématique, une théorie logique T2 est une extension conservatrice (ou conservative) d'une théorie T1 si le langage de T2 étend le langage de T1, si chaque théorème de T1 est un théorème de T2 et si tout théorème de T2 qui est dans le langage de T1 est déjà un théorème de T1. Une extension propre est une extension non conservative. si T2 est une extension conservatrice de T1, et si T1 est cohérente, alors T2 est également cohérente. Le démonstrateur automatique Isabelle adopte cette méthodologie en fournissant un langage pour les extensions conservatrices par définition. extensions conservatrices par définition.
, 수리논리학에서 보존적 확장(保存的擴張, 영어: conservative extension)은 주어진 이론을 확장하되, 원래 이론의 언어로서 나타낼 수 있는 모든 명제의 증명 가능성 여부가 바뀌지 않게 하는 확장이다.
, In logica matematica, nell'ambito della te … In logica matematica, nell'ambito della teoria della dimostrazione, un'estensione conservativa di una teoria logica T1 è una teoria T2 tale che:
* tutti i simboli di T1 sono presenti anche in T2
* ogni teorema di T1 è anche un teorema di T2
* ogni teorema di T2 esprimibile usando soltanto il linguaggio di T1 è un teorema di T1. Nella teoria dei modelli, T2 si dice un'estensione conservativa di T1 se ogni modello di T1 può essere esteso in un modello di T2. Tutte le estensioni conservative nel senso della teoria dei modelli lo sono anche nella definizione della teoria della dimostrazione.inizione della teoria della dimostrazione.
, In mathematical logic, a conservative exte … In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory. Similarly, a non-conservative extension is a supertheory which is not conservative, and can prove more theorems than the original. More formally stated, a theory is a (proof theoretic) conservative extension of a theory if every theorem of is a theorem of , and any theorem of in the language of is already a theorem of . An extension which is not conservative may be called a proper extension.ervative may be called a proper extension.
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| rdfs:label |
Estensione conservativa
, 保守扩展
, 보존적 확장
, Extension conservatrice
, Conservative extension
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