We introduce a modal expansion of paraconsistent Nelson logic that is also as a generalization of the Belnapian modal logic recently introduced by Odintsov and Wansing. We prove algebraic completeness theorems for both logics, defining and axiomatizing the corresponding algebraic semantics. We provide a representation for these algebras in terms of twiststructures, generalizing a known result on the representation of the algebraic counterpart of paraconsistent Nelson logic.

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 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. (shrink)