A Hybridization of Irreflexive Modal Logics

This paper discusses a bimodal hybrid language with a sub-modality (called the irreflexive modality) associated with the intersection of the accessibility relation R and the inequality ≠. First, we provide the Hilbert-style axiomatizations (with and without the COV-rule) for logics of our language, and prove the Kripke completeness and the finite frame property for them. Second, with respect to the frame expressive power, we compare our language containing the irreflexive modality with the hybrid languages H and H(E). Finally, we establish the Goldblatt-Thomason-style characterization for our language.