Global caching for coalgebraic description logics

Authors:
Rajeev Goré;Clemens Kupke;Dirk Pattinson;Lutz Schröder
Affiliations:
Computer Science Laboratory, The Australian National University;Department of Computing, Imperial College London;Department of Computing, Imperial College London;DFKI Bremen and Department of Computer Science, Universität Bremen
Venue:
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Year:
2010

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Abstract

Coalgebraic description logics offer a common semantic umbrella for extensions of description logics with reasoning principles outside relational semantics, e.g. quantitative uncertainty, non-monotonic conditionals, or coalitional power. Specifically, we work in coalgebraic logic with global assumptions (i.e. a general TBox), nominals, and satisfaction operators, and prove soundness and completeness of an associated tableau algorithm of optimal complexity ExpTime. The algorithm uses the (known) tableau rules for the underlying modal logics, and is based on on global caching, which raises hopes of practically feasible implementation. Instantiation of this result to concrete logics yields new algorithms in all cases including standard relational hybrid logic.