Public announcement logic with distributed knowledge

Abstract

While dynamic epistemic logics with common knowledge have been extensively studied, dynamic epistemic logics with distributed knowledge have so far received far less attention. In this paper we study extensions of public announcement logic (P AL) with distributed knowledge, in particular their expressivity and axiomatisations. P AL extended only with distributed knowledge is not more expressive than standard epistemic logic with distributed knowledge. Our focus is therefore on P ACD, the result of adding both common and distributed knowledge to P AL, which is more expressive than each of its component logics. Our main result is a completeness result for P ACD. The axiomatisation is not surprising: it is the combination of well-known axioms. The completeness proof, however, is not trivial, and requires novel combinations and extensions of techniques for dealing with S5 knowledge, distributed knowledge, common knowledge and public announcements at the same time. © 2011 Springer-Verlag.