## PSPACE bounds for rank 1 modal logics (2006)

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Venue: | IN LICS’06 |

Citations: | 26 - 15 self |

### BibTeX

@INPROCEEDINGS{Schröder06pspacebounds,

author = {Lutz Schröder and Dirk Pattinson},

title = {PSPACE bounds for rank 1 modal logics},

booktitle = {IN LICS’06},

year = {2006},

publisher = {}

}

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### Abstract

For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank-1 logics enjoy a shallow model property and thus are, under mild assumptions on the format of their axiomatisation, in PSPACE. This leads to a unified derivation of tight PSPACE-bounds for a number of logics including K, KD, coalition logic, graded modal logic, majority logic, and probabilistic modal logic. Our generic algorithm moreover finds tableau proofs that witness pleasant prooftheoretic properties including a weak subformula property. This generality is made possible by a coalgebraic semantics, which conveniently abstracts from the details of a given model class and thus allows covering a broad range of logics in a uniform way.