Consistent Query Answering over Existential Rules with Open and Closed Predicates

We study Consistent Query Answering (CQA) over knowledge bases with existential rules. Specifically, we propose a novel framework for CQA that combines previous approaches, allowing for the simultaneous presence of both open and closed predicates, i.e. predicates interpreted under open- and closed-world assumption, respectively. We establish the data complexity of answering unions of conjunctive queries in such a new framework under the so-called AR semantics and for different classes of existential rules. We also provide new complexity results for the standard (i.e. non-inconsistency tolerant) query answering in the presence of both open and closed predicates. Our results show that, for certain classes of rules, the complexity of CQA matches that of non-inconsistency-tolerant query answering.