Non axiomatizability of the finitary Lukasiewicz modal logic

Abstrakt

Many-valued modal logics, understood as the logics arising from Kripke models evaluated over residuated lattices, is a field under development in which many questions remain open. In particular, while their semantic definition is clear, formulating corresponding axiomatic systems for these logics is one of the problems under study. We focus in this work on a problem arising from [8, 7] concerning the modal logic of the Kripke frames with a crisp accessibility relation evaluated over the standard Lukasiewicz algebra [0, 1] L.