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Abstract: The methods used to establish PSPACE-bounds for modal logics can roughly begrouped into two classes: syntax driven methods establish that exhaustive proofsearch can be performed in polynomial space whereas semantic approachesdirectly construct shallow models. In this paper, we follow the latter approachand establish generic PSPACE-bounds for a large and heterogeneous class ofmodal logics in a coalgebraic framework. In particular, no completeaxiomatisation of the logic under scrutiny is needed. This does not onlycomplement our earlier, syntactic, approach conceptually, but also covers awide variety of new examples which are difficult to harness by purely syntacticmeans. Apart from re-proving known complexity bounds for a large variety ofstructurally different logics, we apply our method to obtain previously unknownPSPACE-bounds for Elgesem-s logic of agency and for graded modal logic overreflexive frames.



Author: Lutz Schröder, Dirk Patinson

Source: https://arxiv.org/







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