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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 Multimodal logic ： ウィキペディア英語版 Multimodal logic A multimodal logic is a modal logic that has more than one primitive modal operator. They find substantial applications in theoretical computer science. A modal logic with ''n'' primitive unary modal operators $\backslash Box\_i,\; i\backslash in\; \backslash$ is called an ''n''-modal logic. Given these operators and negation, one can always add $\backslash Diamond\_i$ modal operators defined as $\backslash Diamond\_i\; P$ if and only if $\backslash lnot\; \backslash Box\_i\; \backslash lnot\; P$. The first substantive example of a 2-modal logic is perhaps Arthur Prior's tense logic, with two modalities, F and P, corresponding to "sometime in the future" and "sometime in the past". A logic with infinitely many modalities is (propositional) dynamic logic, introduced in 1976 and having a separate modal operator for every regular expression. A version of temporal logic introduced in 1977 and intended for program verification has two modalities, corresponding to dynamic logic's () and () modalities for a single program ''A'', understood as the whole universe taking one step forwards in time. The term "multimodal logic" itself was not introduced until 1980. Another example of a multimodal logic is the Hennessy-Milner logic, itself a fragment of the more expressive modal μ-calculus, which additionally is also a fixed-point logic. Multimodal logic can be used also to formalize a kind of knowledge representation: the motivation of epistemic logic is allowing several agents (they are regarded as subjects capable of forming beliefs, knowledge); and managing the belief or knowledge of each agent, so that epistemic assertions can be formed about them. The modal operator $\backslash Box$ must be capable of bookkeeping the cognition of each agent, thus $\backslash Box\_i$ must be indexed on the set of the agents. The motivation is that $\backslash Box\_i\; \backslash alpha$ should assert "The subject ''i'' has knowledge about $\backslash alpha$ being true". But it can be used also for formalizing "the subject ''i'' believes $\backslash alpha$". For formalization of meaning based on the possible world semantics approach, a multimodal generalization of Kripke semantics can be used: instead of a single "common" accessibility relation, there is a series of them indexed on the set of agents.〔Ferenczi 2002: 257〕 == Notes == 〔 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「Multimodal logic」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.