A map of common knowledge logics

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

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)57-86
Number of pages30
JournalStudia Logica
Volume71
Issue number1
Publication statusPublished - 2002
Externally publishedYes

Keywords

  • Common knowledge extension
  • Embedding theorem
  • Epistemic propositional and predicate logics
  • Fixed-point approach
  • Infinitary approach
  • Kripke-completeness
  • Kripke-incompleteness

ASJC Scopus subject areas

  • Logic

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  • Cite this

    Kaneko, M., Nagashima, T., Suzuki, N. Y., & Tanaka, Y. (2002). A map of common knowledge logics. Studia Logica, 71(1), 57-86.