A Hierarchy of Modal Logics — Extended version —

When dealing with different systems of modal logic, it is often necessary to know about the interrelations between them. This paper focuses on and gives the inclusion structure of a larger collection of modal systems, among them the most common logics. As a first step, we find and prove all inclusions between the systems in question, using their axiomatization. Subsequently, we show for all remaining pairs of logics that one is not contained in the other. For the latter step we use their semantic properties.