The advent of the Semantic Web has made the problem of inconsistency management especially relevant; in this domain, a family of ontology languages called Datalog+/– has been recently developed for representing and reasoning over lightweight ontologies. In this talk, we review different semantics for query answering in inconsistent Datalog+/– ontologies. The first of these, Consistent Query Answering (CQA), was first developed for relational databases almost two decades ago and has become the de facto standard semantics for query answering in the presence of inconsistency. Recently, in the setting of OBDA, where tractability is paramount, several (sound and complete) approximations to CQA have been developed. Unfortunately, in many cases tractability is achieved either by crippling the expressiveness of the language or by adopting very simple semantics. We discuss the relationship among the different semantics and their respective complexity for answering (unions of) conjunctive queries. Finally, we discuss alternatives that try to break away from the "repair-based" models in order to obtain (potentially) higher quality answers.
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