U. Hustadt, B. Motik, and U. Sattler (2005a): ``A Decomposition Rule for Decision Procedures by Resolution-Based Calculi.'' In F. Baader and A. Voronkov, editors, Proceedings of the 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning LPAR 2004 (Montevideo, Uruguay, March 14-18, 2005), pp. 21-35. LNAI 3452, Springer.
Abstract, BibTeX, Abstract + PDF (via Springer).

Resolution-based calculi are among the most widely used calculi for theorem proving in first-order logic. Numerous refinements of resolution are nowadays available, such as e.g. basic superposition, a calculus highly optimized for theorem proving with equality. However, even such an advanced calculus does not restrict inferences enough to obtain decision procedures for complex logics, such as SHIQ. In this paper, we present a new decomposition inference rule, which can be combined with any resolution-based calculus compatible with the standard notion of redundancy. We combine decomposition with basic superposition to obtain three new decision procedures: (i) for the description logic SHIQ, (ii) for the description logic ALCHIQb, and (iii) for answering conjunctive queries over SHIQ knowledge bases. The first two procedures are worst-case optimal and, based on the vast experience in building efficient theorem provers, we expect them to be suitable for practical usage. [an error occurred while processing this directive]