A map of common knowledge logics

Mamoru Kaneko*, Takashi Nagashima, Nobu Yuki Suzuki, Yoshihito Tanaka

*この研究の対応する著者

研究成果: Article査読

6 被引用数 (Scopus)

抄録

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.

本文言語English
ページ(範囲)57-86
ページ数30
ジャーナルStudia Logica
71
1
出版ステータスPublished - 2002
外部発表はい

ASJC Scopus subject areas

  • 論理

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