Many-valued multi-modal logics, satisfiability problem

This paper investigates many-valuated multi-modal logics. The suggested semantics consists of relational Kripke–Hintikka models which have various accessibility relations and distinct valuations for propositional statements (letters). So we study a multi-agent approach when each agent has its own accessibility relation and also its own valuation for propositional letters. We suggest the rules for computation of truth values of formulas, illustrate our approach, and study the satisfiability problem.
Using a modification of the filtration technique, we obtain a solution for satisfiability problem in basic but most important wide classes of multi-valued multi-modal models. We comment on possible applications and describe open problems.