In an open, constantly changing and collaborative environment like the forthcoming Semantic Web, it is reasonable to expect that knowledge sources will contain noise and inaccuracies. It is well known, as the logical foundation of the Semantic Web, description logic is lack of the ability of tolerating inconsistent or incomplete data. Recently, the ability of paraconsistent approaches in Semant...

This article builds on work by Bolander and Blackburn [7] on terminating tableau systems for the minimal hybrid logic K. We provide (for the basic uni-modal hybrid language) terminating tableau systems for a number of non-transitive hybrid logics extending K, such as the logic of irreflexive frames, antisymmetric frames, and so on; these systems don’t employ loop-checks. We also provide (for hy...

We present sound and complete tableau calculi for the class of regular grammar logics and a class eRG of extended regular grammar logics which contains useful epistemic logics for reasoning about beliefs of agents. Our tableau rules use a special feature called automaton-modal formulae which are similar to formulae of automaton propositional dynamic logic. Our calculi are cut-free and have the ...