1. On the Logic of Common Belief and Common Knowledge.Luc Lismont & Philippe Mongin - 1994 - Theory and Decision 37 (1):75-106.
    The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections (...)
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    La Connaissance Commune En Logique Modale.Luc Lismont - 1993 - Mathematical Logic Quarterly 39 (1):115-130.
    The problem of Common Knowledge will be considered in two classes of models: a class K.* of Kripke models and a class S of Scott models. Two modal logic systems will be defined. Those systems, KC and MC, include an axiomatisation of Common Knowledge. We prove determination of each system by the corresponding class of models. MSC: 03B45, 68T25.
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  3. A Non-Minimal but Very Weak Axiomatization of Common Belief.Luc Lismont & Philippe Mongin - 1994 - Artificial Intelligence 70 (1-2):363-374.