We study consistent query answering over knowledge bases expressed by existential rules. Specifically, we establish the data complexity of consistent query answering and repair checking under tuple-deletion semantics for a general class of disjunctive existential rules and for several subclasses thereof (acyclic, linear, full, guarded, and sticky). In particular, we identify several cases in which the above problems are tractable or even first-order rewritable, and present new query rewriting techniques that can be the basis for practical inconsistency-tolerant query answering systems.
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