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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 Negation normal form ： ウィキペディア英語版 Negation normal form In mathematical logic, a formula is in negation normal form if the negation operator ($\backslash lnot$, ) is only applied to variables and the only other allowed Boolean operators are conjunction ($\backslash land$, ) and disjunction ($\backslash lor$, ). Negation normal form is not a canonical form: for example, $a\; \backslash land\; (b\backslash lor\; \backslash lnot\; c)$ and $(a\; \backslash land\; b)\; \backslash lor\; (a\; \backslash land\; \backslash lnot\; c)$ are equivalent, and are both in negation normal form. In classical logic and many modal logics, every formula can be brought into this form by replacing implications and equivalences by their definitions, using De Morgan's laws to push negation inwards, and eliminating double negations. This process can be represented using the following rewrite rules: :$\backslash lnot\; (\backslash forall\; x.\; G)\; \backslash to\; \backslash exists\; x.\; \backslash lnot\; G$ :$\backslash lnot\; (\backslash exists\; x.\; G)\; \backslash to\; \backslash forall\; x.\; \backslash lnot\; G$ :$\backslash lnot\; \backslash lnot\; G\; \backslash to\; G$ :$\backslash lnot\; (G\_1\; \backslash land\; G\_2)\; \backslash to\; (\backslash lnot\; G\_1)\; \backslash lor\; (\backslash lnot\; G\_2)$ :$\backslash lnot\; (G\_1\; \backslash lor\; G\_2)\; \backslash to\; (\backslash lnot\; G\_1)\; \backslash land\; (\backslash lnot\; G\_2)$ A formula in negation normal form can be put into the stronger conjunctive normal form or disjunctive normal form by applying distributivity. ==Examples and counterexamples== The following formulae are all in negation normal form: :$(A\; \backslash vee\; B)\; \backslash wedge\; C$ :$(A\; \backslash wedge\; (\backslash lnot\; B\; \backslash vee\; C)\; \backslash wedge\; \backslash lnot\; C)\; \backslash vee\; D$ :$A\; \backslash vee\; \backslash lnot\; B$ :$A\; \backslash wedge\; \backslash lnot\; B$ The first example is also in conjunctive normal form and the last two are in both conjunctive normal form and disjunctive normal form, but the second example is in neither. The following formulae are not in negation normal form: :$A\; \backslash Rightarrow\; B$ :$\backslash lnot\; (A\; \backslash vee\; B)$ :$\backslash lnot\; (A\; \backslash wedge\; B)$ :$\backslash lnot\; (A\; \backslash vee\; \backslash lnot\; C)$ They are however respectively equivalent to the following formulae in negation normal form: :$\backslash lnot\; A\; \backslash vee\; B$ :$\backslash lnot\; A\; \backslash wedge\; \backslash lnot\; B$ :$\backslash lnot\; A\; \backslash vee\; \backslash lnot\; B$ :$\backslash lnot\; A\; \backslash wedge\; C$ 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「Negation normal form」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.