  In this work we study the decidability of the global modal logic arising from
Kripke frames evaluated on certain residuated lattices (including all BL
algebras), known in the literature as crisp modal many-valued logics. We
exhibit a large family of these modal logics that are undecidable, in
opposition to classical modal logic and to the propositional logics defined
over the same classes of algebras. These include the global modal logics
arising from the standard Lukasiewicz and Product algebras. Furthermore, it is
shown that global modal Lukasiewicz and Product logics are not recursively
axiomatizable. We conclude the paper by solving negatively the open question of
whether a global modal logic coincides with the local modal logic closed under
the unrestricted necessitation rule.
