The advent of the Semantic Web has made the problem of inconsistency management especially relevant. Datalog+/- is a family of ontology languages that is in particular useful for representing and reasoning over lightweight ontologies in the Semantic Web. In this paper, we study different semantics for query answering in inconsistent Datalog+/- ontologies. We develop a general framework for inconsistency management in Datalog+/- ontologies based on incision functions from belief revision, in which we can characterize several query answering semantics as special cases: (i) consistent answers, originally developed for relational databases and recently adopted for some classes of description logics (DLs), (ii) intersection semantics, a sound approximation of consistent answers, and (iii) lazy consistent answers, a novel alternative semantics that offers a good compromise between quality of answers and computation time. We also provide complexity results for query answering under the different semantics, including data tractability results.
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