From classical to consistent query answering under existential rules

Querying inconsistent ontologies is an intriguing new problem that gave rise to a flourishing research activity in the description logic (DL) community. The computational complexity of consistent query answering under the main DLs is rather well understood; however, little is known about existential rules. The goal of the current work is to perform an in-depth analysis of the complexity of consistent query answering under the main decidable classes of existential rules enriched with negative constraints. Our investigation focuses on the standard inconsistency-tolerant semantics, namely, the AR semantics. We establish generic complexity results, which demonstrate the tight connection between classical and consistent query answering. These results allow us to obtain in a uniform way a relatively complete picture of the complexity of our problem.