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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 Destructive dilemma ： ウィキペディア英語版 Destructive dilemma Destructive dilemma〔Hurley, Patrick. A Concise Introduction to Logic With Ilrn Printed Access Card. Wadsworth Pub Co, 2008. Page 361〕〔Moore and Parker〕 is the name of a valid rule of inference of propositional logic. It is the inference that, if ''P'' implies ''Q'' and ''R'' implies ''S'' and either ''Q'' is false or ''S'' is false, then either ''P'' or ''R'' must be false. In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents has to be false. ''Destructive dilemma'' is the disjunctive version of ''modus tollens''. The disjunctive version of ''modus ponens'' is the constructive dilemma. The rule can be stated: :$\backslash frac$ where the rule is that wherever instances of "$P\; \backslash to\; Q$", "$R\; \backslash to\; S$", and "$\backslash neg\; Q\; \backslash or\; \backslash neg\; S$" appear on lines of a proof, "$\backslash neg\; P\; \backslash or\; \backslash neg\; R$" can be placed on a subsequent line. ==Formal notation== The ''destructive dilemma'' rule may be written in sequent notation: : $(P\; \backslash to\; Q),\; (R\; \backslash to\; S),\; (\backslash neg\; Q\; \backslash or\; \backslash neg\; S)\; \backslash vdash\; (\backslash neg\; P\; \backslash or\; \backslash neg\; R)$ where $\backslash vdash$ is a metalogical symbol meaning that $\backslash neg\; P\; \backslash or\; \backslash neg\; R$ is a syntactic consequence of $P\; \backslash to\; Q$, $R\; \backslash to\; S$, and $\backslash neg\; Q\; \backslash or\; \backslash neg\; S$ in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: :$(((P\; \backslash to\; Q)\; \backslash and\; (R\; \backslash to\; S))\; \backslash and\; (\backslash neg\; Q\; \backslash or\; \backslash neg\; S))\; \backslash to\; (\backslash neg\; P\; \backslash or\; \backslash neg\; R)$ where $P$, $Q$, $R$ and $S$ are propositions expressed in some formal system. 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「Destructive dilemma」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.