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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 Biconditional elimination ： ウィキペディア英語版 Biconditional elimination Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional. If $(P\; \backslash leftrightarrow\; Q)$ is true, then one may infer that $(P\; \backslash to\; Q)$ is true, and also that $(Q\; \backslash to\; P)$ is true. For example, if it's true that I'm breathing if and only if I'm alive, then it's true that if I'm breathing, I'm alive; likewise, it's true that if I'm alive, I'm breathing. The rules can be stated formally as: :$\backslash frac$ and :$\backslash frac$ where the rule is that wherever an instance of "$(P\; \backslash leftrightarrow\; Q)$" appears on a line of a proof, either "$(P\; \backslash to\; Q)$" or "$(Q\; \backslash to\; P)$" can be placed on a subsequent line; == Formal notation == The ''biconditional elimination'' rule may be written in sequent notation: :$(P\; \backslash leftrightarrow\; Q)\; \backslash vdash\; (P\; \backslash to\; Q)$ and :$(P\; \backslash leftrightarrow\; Q)\; \backslash vdash\; (Q\; \backslash to\; P)$ where $\backslash vdash$ is a metalogical symbol meaning that $(P\; \backslash to\; Q)$, in the first case, and $(Q\; \backslash to\; P)$ in the other are syntactic consequences of $(P\; \backslash leftrightarrow\; Q)$ in some logical system; or as the statement of a truth-functional tautology or theorem of propositional logic: :$(P\; \backslash leftrightarrow\; Q)\; \backslash to\; (P\; \backslash to\; Q)$ :$(P\; \backslash leftrightarrow\; Q)\; \backslash to\; (Q\; \backslash to\; P)$ 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「Biconditional elimination」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.