  In this paper, we explore the issue of inconsistency handling over
prioritized knowledge bases (KBs), which consist of an ontology, a set of
facts, and a priority relation between conflicting facts. In the database
setting, a closely related scenario has been studied and led to the definition
of three different notions of optimal repairs (global, Pareto, and completion)
of a prioritized inconsistent database. After transferring the notions of
globally-, Pareto- and completion-optimal repairs to our setting, we study the
data complexity of the core reasoning tasks: query entailment under
inconsistency-tolerant semantics based upon optimal repairs, existence of a
unique optimal repair, and enumeration of all optimal repairs. Our results
provide a nearly complete picture of the data complexity of these tasks for
ontologies formulated in common DL-Lite dialects. The second contribution of
our work is to clarify the relationship between optimal repairs and different
notions of extensions for (set-based) argumentation frameworks. Among our
results, we show that Pareto-optimal repairs correspond precisely to stable
extensions (and often also to preferred extensions), and we propose a novel
semantics for prioritized KBs which is inspired by grounded extensions and
enjoys favourable computational properties. Our study also yields some results
of independent interest concerning preference-based argumentation frameworks.
