A Nonminimal But Very Weak Axiomatization of Common Belief

The paper introduces a modal logic system of individual and common belief which is shown to be sound and complete with respect to a version of Neighbourhood semantics. This axiomatization of common belief is the weakest of all those currently available: it dispenses with even the Monotonicity rule of individual belief. It is non-minimal in that it does not use just the Equivalence rule but the conjunction of the latter with the specially devised rule of C-Restricted Monotonicity