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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 Material implication (rule of inference) ： ウィキペディア英語版 Material implication (rule of inference) In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction if and only if the antecedent is negated. The rule states that ''P implies Q'' is logically equivalent to ''not-P or Q'' and can replace each other in logical proofs. :$P\; \backslash to\; Q\; \backslash Leftrightarrow\; \backslash neg\; P\; \backslash or\; Q$ Where "$\backslash Leftrightarrow$" is a metalogical symbol representing "can be replaced in a proof with." == Formal notation == The ''material implication'' rule may be written in sequent notation: :$(P\; \backslash to\; Q)\; \backslash vdash\; (\backslash neg\; P\; \backslash or\; Q)$ where $\backslash vdash$ is a metalogical symbol meaning that $(\backslash neg\; P\; \backslash or\; Q)$ is a syntactic consequence of $(P\; \backslash to\; Q)$ in some logical system; or in rule form: :$\backslash frac$ 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 "$\backslash neg\; P\; \backslash or\; Q$"; or as the statement of a truth-functional tautology or theorem of propositional logic: :$(P\; \backslash to\; Q)\; \backslash to\; (\backslash neg\; P\; \backslash or\; Q)$ 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「Material implication (rule of inference)」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.