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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Principle of explosion ： ウィキペディア英語版 Principle of explosion The principle of explosion (Latin: ''ex falso (sequitur) quodlibet'' (EFQ), "from falsehood, anything (follows)", or ''ex contradictione (sequitur) quodlibet'' (ECQ), "from contradiction, anything (follows)"), or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction.〔Carnielli, W. and Marcos, J. (2001) ("Ex contradictione non sequitur quodlibet" ) ''Proc. 2nd Conf. on Reasoning and Logic'' (Bucharest, July 2000)〕 That is, once a contradiction has been asserted, any proposition (including their negations) can be inferred from it. As a demonstration of the principle, consider two contradictory statements – “All lemons are yellow” and "Not all lemons are yellow", and suppose (for the sake of argument) that both are simultaneously true. If that is the case, anything can be proven, e.g. "Santa Claus exists", by using the following argument: # We know that "All lemons are yellow" as it is defined to be true. # Therefore, the statement that (“All lemons are yellow" OR "Santa Claus exists”) must also be true, since the first part is true. # However, if "Not all lemons are yellow" (and this is also defined to be true), Santa Claus must exist – otherwise statement 2 would be false. It has thus been "proven" that Santa Claus exists. The same could be applied to any assertion, including the statement "Santa Claus does not exist". The principle is not a universal rule; rather it exists as a consequence of a choice of which logic to use. It does not appear in some paraconsistent logics which allow localised 'gluts' of contradictory statements to be proved without affecting other proofs. In artificial intelligence and models of human reasoning it is common for such logics to be used. This can also occur in formal science, for example quantum mechanics and relativity lead to contradictions in extreme environments, but these contradictions do not imply that Santa exists – only that there are some scenarios where one or both theories are in need of alteration. Truth maintenance systems are AI models which try to capture this process. ==Symbolic representation== The principle of explosion can be expressed in the following way (where "$\backslash vdash$" symbolizes the relation of logical consequence and "$\backslash bot$" symbolizes a contradiction) : : $\backslash \; \backslash vdash\; \backslash psi$ : ''or'' : $\backslash bot\; \backslash to\; P$. This can be read as, "If one claims something ($\backslash phi\backslash ,$) and its negation ($\backslash lnot\; \backslash phi$), one can logically derive ''any'' conclusion ($\backslash psi$)." 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Principle of explosion」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.