Abstract

We study modal completeness and incompleteness of several sublogics of the interpretability logic. We introduce the sublogic, and prove that is sound and complete with respect to Veltman prestructures which are introduced by Visser. Moreover, we prove the modal completeness of twelve logics between and with respect to Veltman prestructures. On the other hand, we prove that eight natural sublogics of are modally incomplete. Finally, we prove that these incomplete logics are complete with respect to generalized Veltman prestructures. As a consequence of these investigations, we obtain that the twenty logics studied in this paper are all decidable.