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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 General frame ： ウィキペディア英語版 General frame In logic, general frames (or simply frames) are Kripke frames with an additional structure, which are used to model modal and intermediate logics. The general frame semantics combines the main virtues of Kripke semantics and algebraic semantics: it shares the transparent geometrical insight of the former, and robust completeness of the latter. ==Definition== A modal general frame is a triple $\backslash mathbf\; F=\backslash langle\; F,R,V\backslash rangle$, where $\backslash langle\; F,R\backslash rangle$ is a Kripke frame (i.e., ''R'' is a binary relation on the set ''F''), and ''V'' is a set of subsets of ''F'' which is closed under *the Boolean operations of (binary) intersection, union, and complement, *the operation $\backslash Box$, defined by $\backslash Box\; A=\backslash$. The purpose of ''V'' is to restrict the allowed valuations in the frame: a model $\backslash langle\; F,R,\backslash Vdash\backslash rangle$ based on the Kripke frame $\backslash langle\; F,R\backslash rangle$ is admissible in the general frame F, if :$\backslash \backslash in\; V$ for every propositional variable ''p''. The closure conditions on ''V'' then ensure that $\backslash$ belongs to ''V'' for ''every'' formula ''A'' (not only a variable). A formula ''A'' is valid in F, if $x\backslash Vdash\; A$ for all admissible valuations $\backslash Vdash$, and all points $x\backslash in\; F$. A normal modal logic ''L'' is valid in the frame F, if all axioms (or equivalently, all theorems) of ''L'' are valid in F. In this case we call F an ''L''-frame. A Kripke frame $\backslash langle\; F,R\backslash rangle$ may be identified with a general frame in which all valuations are admissible: i.e., $\backslash langle\; F,R,\backslash mathcal(F)\backslash rangle$, where $\backslash mathcal\; P(F)$ denotes the power set of ''F''. 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「General frame」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.