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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 Sahlqvist formula ： ウィキペディア英語版 Sahlqvist formula In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every Sahlqvist formula is canonical, and corresponds to a first-order definable class of Kripke frames. Sahlqvist's definition characterizes a decidable set of modal formulas with first-order correspondents. Since it is undecidable, by Chagrova's theorem, whether an arbitrary modal formula has a first-order correspondent, there are formulas with first-order frame conditions that are not Sahlqvist (1991 ) (see the examples below). Hence Sahlqvist formulas define only a (decidable) subset of modal formulas with first-order correspondents. == Definition == Sahlqvist formulas are built up from implications, where the consequent is ''positive'' and the antecedent is of a restricted form. * A ''boxed atom'' is a propositional atom preceded by a number (possibly 0) of boxes, i.e. a formula of the form $\backslash Box\backslash cdots\backslash Box\; p$ (often abbreviated as $\backslash Box^i\; p$ for ). * A ''Sahlqvist antecedent'' is a formula constructed using ∧, ∨, and $\backslash Diamond$ from boxed atoms, and negative formulas (including the constants ⊥, ⊤). * A ''Sahlqvist implication'' is a formula ''A'' → ''B'', where ''A'' is a Sahlqvist antecedent, and ''B'' is a positive formula. * A ''Sahlqvist formula'' is constructed from Sahlqvist implications using ∧ and $\backslash Box$ (unrestricted), and using ∨ on formulas with no common variables. 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「Sahlqvist formula」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.