Several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. The first contribution of this paper is a practical approach for computing the query answers under three well-known such semantics, namely the AR, IAR and brave semantics, in the lightweight description logic DL-LiteR. We show that query answering under the intractable AR semantics can be performed efficiently by using IAR and brave semantics as tractable approximations and encoding the AR entailment problem as a propositional satisfiability (SAT) problem. The second issue tackled in this work is explaining why a tuple is a (non-)answer to a query under these semantics. We define explanations for positive and negative answers under the brave, AR and IAR semantics. We then study the computational properties of explanations in DL-LiteR. For each type of explanation, we analyze the data complexity of recognizing (preferred) explanations and deciding if a given assertion is relevant or necessary. We establish tight connections between intractable explanation problems and variants of SAT, enabling us to generate explanations by exploiting solvers for Boolean satisfaction and optimization problems. Finally, we empirically study the efficiency of our query answering and explanation framework using a benchmark we built upon the well-established LUBM benchmark.

Abstract. An important issue that arises when querying description logic (DL) knowledge bases is how to handle the case in which the knowledge base is inconsistent. Indeed, while it may be reasonable to assume that the TBox (ontology) has been properly debugged, the ABox (data) will typically be very large and subject to frequent modifications, both of which make errors likely. As standard DL semantics is useless in such circumstances (everything is entailed from a contradiction), several alternative inconsistency-tolerant semantics have been proposed with the aim of providing meaningful answers to queries in the presence of such data inconsistencies. In the first part of this chapter, we present and compare these inconsistency-tolerant semantics, which can be applied to any DL (or ontology language). The second half of the chapter summarizes what is known about the computational properties of these semantics and gives an overview of the main algorithmic techniques and existing systems, focusing on DLs of the DL-Lite family.