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.
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The second and third author supported by EPSRC grant EP/F031173/1. The last author supported by BMBF grant FormalSafe (FKZ 01IW07002).
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Goré, R., Kupke, C., Pattinson, D., Schröder, L. (2010). Global Caching for Coalgebraic Description Logics. In: Giesl, J., Hähnle, R. (eds) Automated Reasoning. IJCAR 2010. Lecture Notes in Computer Science(), vol 6173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14203-1_5
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DOI: https://doi.org/10.1007/978-3-642-14203-1_5
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