A map of common knowledge logics

Studia Logica 71 (1):57-86 (2002)
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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.

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Citations of this work

Common Knowledge and Argumentation Schemes .Fabrizio Macagno & Douglas Walton - 2005 - Studies in Communication Sciences 5 (2):1-22.

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References found in this work

Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
First order common knowledge logics.Frank Wolter - 2000 - Studia Logica 65 (2):249-271.
Game logic and its applications I.Mamoru Kaneko & Takashi Nagashima - 1996 - Studia Logica 57 (2-3):325 - 354.
Kripke Completeness of Infinitary Predicate Multimodal Logics.Yoshihito Tanaka - 1999 - Notre Dame Journal of Formal Logic 40 (3):326-340.

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