A Hybrid Public Announcement Logic with Distributed Knowledge

In this paper the machinery of Hybrid Logic and the logic of public announcements are merged. In order to bring the two logics together properly the underlying hybrid logic has been changed such that nominals only partially denote states. The hybrid logic contains nominals, satisfaction operators, the downarrow binder as well as the global modality. Following this, an axiom system for the Hybrid Public Announcement Logic is presented and using reduction axioms general completeness (in the usual style of Hybrid Logic) is proved. The general completeness allows for an easy way of adding distributed knowledge. Furthermore it turns out that distributed knowledge is definable using satisfaction operators and the downarrow binder. The standard way of adding distributed knowledge using reduction axioms is also discussed and generalized to other modalities sharing properties with the distributed knowledge modality.