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Reasoning with Boolean Aboxes List of Figures

ABoxes in Description Logics are used to represent factual knowledge of the world. In many situations an ABox is not enough to represent the knowledge of the world under consideration, as there is just an implicit boolean AND (∧) operator between each ABox assertion in the ABox. A Boolean ABox allows us to state Boolean combination of ABox assertions. The present work deals with the consistency problem of Boolean ABoxes in Description Logics (DLs). Five years ago, a reduction algorithm to check consistency of ALC Boolean ABoxes has been introduced, in which an ALC Boolean ABox is reduced to a satisfiability preserving knowledge base, possibly in a more expressive description logic. We also argue that the reduction algorithm can be extended to check consistency of ALCO Boolean ABoxes. Motivated by ongoing research in Satisfiability Modulo Theory (SMT), we applied the DPLL(T) approach of SMT to check consistency of Boolean ABoxes. We have implemented a SAT solver based on DPLL procedure with state-of-the-art performance enhancing techniques like backjumping and conflict-driven-lemmalearning. By interconnecting the SAT solver with a DL reasoner using a special communication strategy, we developed a DPLL(T) solver to check consistency of ALCO Boolean ABoxes. We have also implemented a reasoner to check consistency of ALCO Boolean ABoxes based on the reduction algorithm on top of an existing DL reasoner having a reasoning service to check consistency of ALCO ABoxes. In both of the implementations for checking consistency of Boolean ABoxes, Java is used as the programming language. Both of the implementations are tested, compared, and analyzed on the input stemming from the ABox update problem.