Justified and Common Knowledge: Limited Conservativity

Authors:
Evangelia Antonakos
Affiliations:
CUNY Graduate Center, Ph.D. Program in Mathematics, 365 Fifth Avenue, New York, NY 10016, USA
Venue:
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Year:
2007

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Abstract

We consider the relative strengths of three formal approaches to public knowledge: "any fool" knowledge by McCarthy (1970), Common Knowledge by Halpern and Moses (1990), and Justified Knowledge by Artemov (2004). Specifically, we show that epistemic systems with the Common Knowledge modality Care conservative with respect to Justified Knowledge systems on formulas 驴驴 Cφ驴驴, where 驴, φ, and 驴are C-free.