Common belief with the logic of individual belief

Mathematical Logic Quarterly 46 (1):49-52 (2000)
The logic of common belief does not always reflect that of individual beliefs. In particular, even when the individual belief operators satisfy the KD45 logic, the common belief operator may fail to satisfy axiom 5. That is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. We identify the intersubjective restrictions on individual beliefs that are incorporated in axiom 5 for common belief
Keywords Common belief  Negative introspection  Axiom 5  Multi‐modal logic
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DOI 10.1002/(SICI)1521-3870(200001)46:1<49::AID-MALQ49>3.0.CO;2-R
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