As applications of description logics proliferate, efficient reasoning with knowledge bases containing many assertions becomes ever more important. For such cases, we developed a novel reasoning algorithm that reduces a SHIQ knowledge base to a disjunctive datalog program while preserving the set of ground consequences. Queries can then be answered in the resulting program while reusing existing and practically proven optimization techniques of deductive databases, such as join-order optimizations or magic sets. Moreover, we use our algorithm to derive precise data complexity bounds: we show that SHIQ is data complete for NP, and we identify an expressive fragment of SHIQ with polynomial data complexity.

In this paper we give an overview of resolution methods for extended propositional modal logics. We adopt the standard translation approach and consider different resolution refinements which provide decision procedures for the resulting clause sets. Our procedures are based on ordered resolution and selection-based resolution. The logics that we cover are multi-modal logics defined over relations closed under intersection, union, converse and possibly complementation.

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