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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 Universal generalization ： ウィキペディア英語版 Universal generalization In predicate logic, generalization (also universal generalization or universal introduction,〔Copi and Cohen〕〔Hurley〕〔Moore and Parker〕 GEN) is a valid inference rule. It states that if $\backslash vdash\; P(x)$ has been derived, then $\backslash vdash\; \backslash forall\; x\; \backslash ,\; P(x)$ can be derived. ==Generalization with hypotheses== The full generalization rule allows for hypotheses to the left of the turnstile, but with restrictions. Assume Γ is a set of formulas, $\backslash varphi$ a formula, and $\backslash Gamma\; \backslash vdash\; \backslash varphi(y)$ has been derived. The generalization rule states that $\backslash Gamma\; \backslash vdash\; \backslash forall\; x\; \backslash varphi(x)$ can be derived if ''y'' is not mentioned in Γ and ''x'' does not occur in $\backslash varphi$. These restrictions are necessary for soundness. Without the first restriction, one could conclude $\backslash forall\; x\; P(x)$ from the hypothesis $P(y)$. Without the second restriction, one could make the following deduction: #$\backslash exists\; z\; \backslash exists\; w\; (\; z\; \backslash not\; =\; w)$ (Hypothesis) #$\backslash exists\; w\; (y\; \backslash not\; =\; w)$ (Existential instantiation) #$y\; \backslash not\; =\; x$ (Existential instantiation) #$\backslash forall\; x\; (x\; \backslash not\; =\; x)$ (Faulty universal generalization) This purports to show that $\backslash exists\; z\; \backslash exists\; w\; (\; z\; \backslash not\; =\; w)\; \backslash vdash\; \backslash forall\; x\; (x\; \backslash not\; =\; x),$ which is an unsound deduction. 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「Universal generalization」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.