Malinowski modalization, modalization through fibring and the Leibniz hierarchy

We show how various modal systems considered by Malinowski as extensions of classical propositional calculus may be obtained as fibrings of classical propositional calculus and corresponding implicative modal logics, using the fibring framework for combining logics of Fern′andez and Coniglio. Taking advantage of this construction and known results of Malinowski, we draw some useful conclusions concerning some limitations of the fibring process. Finally, Malinowski's constructions are extended to obtain some modal extensions of arbitrary equivalential logics in the context of abstract algebraic logic. These are studied with respect to their algebraic character.