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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 , where 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 , defined by . The purpose of ''V'' is to restrict the allowed valuations in the frame: a model based on the Kripke frame is admissible in the general frame F, if : for every propositional variable ''p''. The closure conditions on ''V'' then ensure that belongs to ''V'' for ''every'' formula ''A'' (not only a variable). A formula ''A'' is valid in F, if for all admissible valuations , and all points . 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 may be identified with a general frame in which all valuations are admissible: i.e., , where 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
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