\(\text{S5}_m (\text{CDE)}\) is a composite propositional logic presented axiomatically, with \(m\) epistemic operators satisfying the S5 modal postulates plus operators \(C\) for ‘it is common knowledge that’, \(D\) for ‘it is distributed knowledge that’, and \(E\) for ‘everybody knows that’. Various segments of this logic have been given semantic characterizations in terms of possible worlds, but it is not a trivial matter to merge the completeness proofs to work for the whole system with respect to an appropriate semantics. The authors carry out the task. In the process they also obtain some new information about finite models and decidability for the composite system and certain of its segments.
For the entire collection see [Zbl 0931.00027].