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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 Rules of passage (logic) ： ウィキペディア英語版 Rules of passage (logic) In mathematical logic, the rules of passage govern how quantifiers distribute over the basic logical connectives of first-order logic. The rules of passage govern the "passage" (translation) from any formula of first-order logic to the equivalent formula in prenex normal form, and vice versa. ==The rules== See Quine (1982: 119, chpt. 23). Let ''Q'' and ''Q'' 'denote ∀ and ∃ or vice versa. β denotes a closed formula in which ''x'' does not appear. The rules of passage then include the following sentences, whose main connective is the biconditional: *$Qx((x))\; \backslash leftrightarrow\; \backslash lnot\; Q\text{'}x((x)).$ *$\backslash \; Qx(\backslash or\; \backslash alpha\; (x))\; \backslash leftrightarrow\; (\backslash beta\; \backslash or\; Qx\; \backslash alpha\; (x)).$ *$\backslash exist\; x((x)\; \backslash or\; \backslash gamma\; (x))\; \backslash leftrightarrow\; (\backslash exist\; x\; \backslash alpha\; (x)\; \backslash or\; \backslash exist\; x\; \backslash gamma\; (x)).$ *$\backslash \; Qx(\backslash and\; \backslash alpha\; (x))\; \backslash leftrightarrow\; (\backslash beta\; \backslash and\; Qx\; \backslash alpha\; (x)).$ *$\backslash forall\; x\; \backslash ,\; (\backslash land\; \backslash gamma(x))\; \backslash leftrightarrow\; (\backslash forall\; x\; \backslash ,\; \backslash alpha(x)\; \backslash land\; \backslash forall\; x\; \backslash ,\; \backslash gamma(x)\; ).$ The following conditional sentences can also be taken as rules of passage: *$\backslash exist\; x((x)\; \backslash and\; \backslash gamma\; (x))\; \backslash rightarrow\; (\backslash exist\; x\; \backslash alpha\; (x)\; \backslash and\; \backslash exist\; x\; \backslash gamma\; (x)).$ *$(\backslash forall\; x\; \backslash ,\; \backslash alpha(x)\; \backslash or\; \backslash forall\; x\; \backslash ,\; \backslash gamma(x))\; \backslash rightarrow\; \backslash forall\; x\; \backslash ,\; (\backslash or\; \backslash gamma(x)).$ *$(\backslash exists\; x\; \backslash ,\; \backslash alpha(x)\; \backslash and\; \backslash forall\; x\; \backslash ,\; \backslash gamma(x))\; \backslash rightarrow\; \backslash exists\; x\; \backslash ,\; (\backslash and\; \backslash gamma(x)).$ "Rules of passage" first appeared in French, in the writings of Jacques Herbrand. Quine employed the English translation of the phrase in each edition of his ''Methods of Logic'', starting in 1950. 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「Rules of passage (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.