Kripke Semantics for Modal Bilattice Logic

We employ the well-developed and powerful techniques of algebraic semantics and Priestley duality to set up a Kripke semantics for a modal expansion of Arieli and Avron's bilattice logic, itself based on Belnap's four-valued logic. We obtain soundness and completeness of a Hilbert-style derivation system for this logic with respect to four-valued Kripke frames, the standard notion of model in this setting. The proof is via intermediary relational structures which are analysed through a topological reading of one of the axioms of the logic. Both local and global consequence on the models are covered.