Monotonic Modal Logics Related to the Von Wright’s Logic of Place

In this paper we introduce the monotonic modal logics M4wn, M4n and MBn obtained from the basic strong monotonic modal logic MON by adding some formulas considered by R. Jansana in [8]. For each logic defined we prove completeness with respect to their characteristic classes of monotonic frames. The canonicity of these logics is proved using the representation theory for monotonic algebras developed in [4]. We also introduce the logics MS4 and MS5 as a monotonic counterpart of the normal logics S4 and S5, respectively. Finally, we prove that there exists a translation of the logic MS4 in M4wn , and a translation of the logic MS5 in M4wn +MBn.