Algebraic Semantics of Refinement Modal Logic

International audienceIn the present paper we develop algebraic semantics of refinement modal logic using duality theory. Refinement modal logic has been introduced by Bozzelli et al.[7]. A Refinement is like a bisimulation, except that from the three relational requirements only 'atoms' and 'back' have to be satisfied. We study the dual notion of refinement on algebras and present algebraic semantics of refinement modal logic. For this end, we proceed as follows: (1) we present the algebraic semantics of action model logic quantifier, (2) we introduce an algebraic model based on semantics of refinement quantifier in terms of refinement relation. Then we show that refinement modal logic is sound and complete with respect to the algebraic semantics introduced