Recently several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases.
Most of these semantics rely on the notion of a repair, defined as an inclusion-maximal subset of the facts (ABox) which is consistent with the ontology (TBox).
In this paper, we study variants of two popular inconsistency-tolerant semantics obtained by replacing classical repairs by various types of preferred repair.
We analyze the complexity of query answering under the resulting semantics, focusing on the lightweight logic DL-Lite_R.
Unsurprisingly, query answering is intractable in all cases, but we nonetheless identify one notion of preferred repair, based upon priority levels, whose data complexity is ``only" coNP-complete.
This leads us to propose an approach combining incomplete tractable methods with calls to a SAT solver.
An experimental evaluation of the approach shows good scalability on realistic cases.



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