  This paper is focused on the study of modal logics defined from valued Kripke
frames, and particularly, on computability and expressibility questions of
modal logics of transitive Kripke frames evaluated over certain residuated
lattices. It is shown that a large family of those logics -- including the ones
arising from the standard MV and Product algebras -- yields an undecidable
consequence relation. Later on, the behaviour of transitive modal Lukasiewicz
logic is compared with that of its non transitive counterpart, exhibiting some
particulars concerning computability and equivalence with other logics. We
conclude the article by showing the undecidability of the validity and the
local SAT questions over transitive models when the Delta operation is added to
the logic.
