Data repair of inconsistent nonmonotonic description logic programs

Combining Description Logic (DL) ontologies and nonmonotonic rules has gained in-creasing attention in the past decade, due to the growing range of applications of DLs. A well-known proposal for such a combination are non-monotonic DL-programs, which support rule-basedreasoning on top of DL ontologies in a loose coupling, using a well-defined query interface. How-ever, inconsistency may easily arise as a result of the interaction of the rules and the ontology,such that no answer set (i.e., model) of a DL-program exists; this makes the program useless. Toovercome this problem, we present a framework for repairing inconsistencies in DL-programs byexchanging formulas of an ontology formulated in DL-LiteA, which is a prominent DL that al-lows for tractable reasoning. Viewing the data part of the ontology as a source of inconsistency,we define program repairs and repair answer sets based on them. We analyze the complexity ofthe notion, and we extend an algorithm for evaluating DL-programs to compute repair answer sets,under optional selection of preferred repairs that satisfy additional constraints. The algorithm in-duces a generalized ontology repair problem, in which the entailment respectively non-entailmentof queries to the ontology, subject to possible updates, must be achieved by a data change. Whilethis problem is intractable in general, we identify several tractable classes of preferred repairs thatare useful in practice. For the class of deletion repairs among them, we optimize the algorithm byreducing query evaluation to constraint matching, based on the novel concept of support set, whichroughly speaking is a portion of the data from which entailment of an ontology query follows. Ourrepair approach is implemented within an answer set program system, using a declarative methodfor repair computation. An experimental evaluation on a suite of benchmark problems shows theeffectiveness of our approach and promising results, both regarding performance and quality of theobtained repairs. While we concentrate on DL-LiteA ontologies, our notions extend to other DLs,for which more general computation approaches may be used. 1Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria;email: {eiter,fink,dasha}@kr.tuwien.ac.at. Acknowledgements: This work has been supported by the Austrian Science Fund (FWF) project P24090. Publication Information: This article is a revised and significantly extended version of the papers [33] and[35] published at IJCAI 2013 and ECAI 2014 respectively.Copyright c© 2015 by the authors 2INFSYS RR 15-03