翻訳と辞書 Words near each other ・ Axiom of determinacy ・ Axiom of empty set ・ Axiom of Equity ・ Axiom of extensionality ・ Axiom of global choice ・ Axiom of infinity ・ Axiom of limitation of size ・ Axiom of Maria ・ Axiom of pairing ・ Axiom of power set ・ Axiom of projective determinacy ・ Axiom of real determinacy ・ Axiom of reducibility ・ Axiom of regularity ・ Axiom of union ・ Axiom S5 ・ Axiom schema ・ Axiom schema of predicative separation ・ Axiom schema of replacement ・ Axiom schema of specification ・ Axiom Telecom ・ Axiom Verge ・ Axiom-man ・ Axioma ・ Axioma Ethica Odini ・ Axiomatic (album) ・ Axiomatic (disambiguation) ・ Axiomatic (story collection) ・ Axiomatic design ・ Axiomatic product development lifecycle Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Axiom S5 ： ウィキペディア英語版 Axiom S5 Axiom (5) extends the modal logic ''M'', to form the modal logic S5. Which in turn, consists of modal logic called K, in honour of Saul Kripke. It is the most basic modal logic, is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the syntax with the modal operator ''necessarily'' $\backslash Box$ and its dual ''possibly'' $\backslash Diamond$. To deal with the new formulas of the form $\backslash Box\; \backslash varphi$ and $\backslash Diamond\; \backslash varphi$, the following rules complement the inference apparatus of K: : the distribution axiom $\backslash Box(\backslash varphi\; \backslash implies\; \backslash psi)\; \backslash implies\; (\backslash Box\; \backslash varphi\; \backslash implies\; \backslash Box\; \backslash psi)$ : necessitation rule $\backslash frac$ The logic ''M'' is K plus the axiom: : (M) $\backslash Box\; \backslash varphi\; \backslash implies\; \backslash varphi$ which restricts the accessibility relation of the Kripke frame to be reflexive. The modal logic S5 is obtained by adding the axiom: : (5) $\backslash Diamond\; \backslash varphi\backslash implies\backslash Box\backslash Diamond\; \backslash varphi$ The (5) axiom restricts the accessibility relation $R$, of the Kripke frame to be euclidean, i.e. $(wRv\; \backslash land\; wRu)\; \backslash implies\; vRu$. In S5 formulas of the form $OOO\backslash ldots\backslash Box\backslash varphi$ can be simplified to $\backslash Box\backslash varphi$ where $OOO\backslash ldots$ is formed by any (finite) number of either $\backslash Box$ or $\backslash Diamond$ operators or both. The same stands for formulas of the form $OOO\backslash ldots\backslash Diamond\backslash varphi$ which can be simplified to $\backslash Diamond\backslash varphi$. ==References== *Chellas, B. F. (1980) ''Modal Logic: An Introduction''. Cambridge University Press. ISBN 0-521-22476-4 *Hughes, G. E., and Cresswell, M. J. (1996) ''A New Introduction to Modal Logic''. Routledge. ISBN 0-415-12599-5 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「Axiom S5」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.