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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 Derivative algebra (abstract algebra) ： ウィキペディア英語版 Derivative algebra (abstract algebra) In abstract algebra, a derivative algebra is an algebraic structure of the signature :<''A'', ·, +, ', 0, 1, D> where :<''A'', ·, +, ', 0, 1> is a Boolean algebra and D is a unary operator, the derivative operator, satisfying the identities: # 0D = 0 # ''x''DD ≤ ''x'' + ''x''D # (''x'' + ''y'')D = ''x''D + ''y''D. xD is called the derivative of x. Derivative algebras provide an algebraic abstraction of the derived set operator in topology. They also play the same role for the modal logic ''wK4'' = ''K'' + ''p''∧?''p'' → ??''p'' that Boolean algebras play for ordinary propositional logic. ==References== * Esakia, L., ''Intuitionistic logic and modality via topology'', Annals of Pure and Applied Logic, 127 (2004) 155-170 * McKinsey, J.C.C. and Tarski, A., ''The Algebra of Topology'', Annals of Mathematics, 45 (1944) 141-191 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「Derivative algebra (abstract algebra)」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.