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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 introduction ： ウィキペディア英語版 Biconditional introduction In propositional logic, biconditional introduction〔Hurley〕〔Moore and Parker〕〔Copi and Cohen〕 is a valid rule of inference. It allows for one to infer a biconditional from two conditional statements. The rule makes it possible to introduce a biconditional statement into a logical proof. If $P\; \backslash to\; Q$ is true, and if $Q\; \backslash to\; P$ is true, then one may infer that $P\; \backslash leftrightarrow\; Q$ is true. For example, from the statements "if I'm breathing, then I'm alive" and "if I'm alive, then I'm breathing", it can be inferred that "I'm breathing if and only if I'm alive". Biconditional introduction is the converse of biconditional elimination. The rule can be stated formally as: :$\backslash frac$ where the rule is that wherever instances of "$P\; \backslash to\; Q$" and "$Q\; \backslash to\; P$" appear on lines of a proof, "$P\; \backslash leftrightarrow\; Q$" can validly be placed on a subsequent line. == Formal notation == The ''biconditional introduction'' rule may be written in sequent notation: :$(P\; \backslash to\; Q),\; (Q\; \backslash to\; P)\; \backslash vdash\; (P\; \backslash leftrightarrow\; Q)$ where $\backslash vdash$ is a metalogical symbol meaning that $P\; \backslash leftrightarrow\; Q$ is a syntactic consequence when $P\; \backslash to\; Q$ and $Q\; \backslash to\; P$ are both in a proof; or as the statement of a truth-functional tautology or theorem of propositional logic: :$((P\; \backslash to\; Q)\; \backslash and\; (Q\; \backslash to\; P))\; \backslash to\; (P\; \backslash leftrightarrow\; Q)$ 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「Biconditional introduction」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.