Common Knowledge in Epistemic Logic With Hypotheses

We recall the epistemic logic S5r for reasoning about knowledge under hypotheses and we investigate the extension of the logic with an operator for common knowledge. The logic S5r is equipped with a modal operator of necessity that can be parameterized with hypotheses representing background assumptions while the extension with the common knowledge operator enables us to describe and reason about common knowledge among agents with possibly different background assumptions. We present an axiomatization of the logic and prove Kripke completeness and decidability results.