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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 Transposition (logic) ： ウィキペディア英語版 Transposition (logic) In propositional logic, transposition〔Moore and Parker〕 is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the truth of "''A'' implies ''B''" the truth of "Not-''B'' implies not-''A''", and conversely.〔Brody, Bobuch A. "Glossary of Logical Terms". ''Encyclopedia of Philosophy''. Vol. 5–6, p. 76. Macmillan, 1973.〕〔Copi, Irving M. ''Symbolic Logic''. 5th ed. Macmillan, 1979. See the Rules of Replacement, pp. 39-40.〕 It is very closely related to the rule of inference modus tollens. It is the rule that: $(P\; \backslash to\; Q)\; \backslash Leftrightarrow\; (\backslash neg\; Q\; \backslash to\; \backslash neg\; P)$ Where "$\backslash Leftrightarrow$" is a metalogical symbol representing "can be replaced in a proof with." == Formal notation == The ''transposition'' rule may be expressed as a sequent: :$(P\; \backslash to\; Q)\; \backslash vdash\; (\backslash neg\; Q\; \backslash to\; \backslash neg\; P)$ where $\backslash vdash$ is a metalogical symbol meaning that $(\backslash neg\; Q\; \backslash to\; \backslash neg\; P)$ is a syntactic consequence of $(P\; \backslash to\; Q)$ in some logical system; or as a rule of inference: :$\backslash frac$ where the rule is that wherever an instance of "$P\; \backslash to\; Q$" appears on a line of a proof, it can be replaced with "$\backslash neg\; Q\; \backslash to\; \backslash neg\; P$"; or as the statement of a truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in ''Principia Mathematica'' as: :$(P\; \backslash to\; Q)\; \backslash to\; (\backslash neg\; Q\; \backslash to\; \backslash neg\; P)$ where $P$ and $Q$ 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「Transposition (logic)」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.