Abstract.
In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe their connections and give dividing examples. Also we find algorithms recognizing these properties for some particular cases.
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Received: 21 October 2000 / Published online: 2 September 2002
Key words or phrases: Multi-agent systems – Non-standard logic – Knowledge representation – Common knowledge – Common information – Fixed points, Kripke models – Modal logic
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Rybakov, V. Refined common knowledge logics or logics of common information. Arch. Math. Logic 42, 179–200 (2003). https://doi.org/10.1007/s001530100134
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DOI: https://doi.org/10.1007/s001530100134