Shallow Models for Non-Iterative Modal Logics

Abstract: The methods used to establish PSPACE-bounds for modal logics can roughly be grouped into two classes: syntax driven methods establish that exhaustive proof search can be performed in polynomial space whereas semantic approaches directly construct shallow models. In this paper, we follow the latter approach and establish generic PSPACE-bounds for a large and heterogeneous class of modal logics in a coalgebraic framework. In particular, no complete axiomatisation of the logic under scrutiny is needed. This does not only complement our earlier, syntactic, approach conceptually, but also covers a wide variety of new examples which are difficult to harness by purely syntactic means. Apart from re-proving known complexity bounds for a large variety of structurally different logics, we apply our method to obtain previously unknown PSPACE-bounds for Elgesem's logic of agency and for graded modal logic over reflexive frames.