Modal extensions of Ł_n-valued logics, coalgebraically

Modal extensions of Łn-valued logics. We study logics with a modal operator and built from a countable set of propositional variables Prop using the connectors ¬,→, , 1 in the usual way. To interpret formulas on structures, we use a (crisp) many-valued generalization of the Kripke models. We fix a positive integer n and we denote by Łn the subalgebra Łn = {0, 1 n , . . . , n−1 n , 1} of the standard MV-algebra 〈[0, 1],¬,→ , 1〉. A frame is a couple 〈W,R〉 where W is a nonempty set and R is an binary relation. We denote by FR the class of frames.