Ontology-Based Data Access with Closed Predicates is Inherently Intractable (Sometimes)

When answering queries in the presence of on-tologies, adopting the closed world assumption for some predicates easily results in intractability. We analyze this situation on the level of individual on-tologies formulated in the description logics DL-Lite and EL and show that in all cases where an-swering conjunctive queries (CQs) with (open and) closed predicates is tractable, it coincides with an-swering CQs with all predicates assumed open. In this sense, CQ answering with closed predicates is inherently intractable. Our analysis also yields a di-chotomy between AC0 and CONP for CQ answer-ing w.r.t. ontologies formulated in DL-Lite and a dichotomy between PTIME and CONP for EL. In-terestingly, the situation is less dramatic in the more expressive description logic ELI, where we find ontologies for which CQ answering is in PTIME, but does not coincide with CQ answering where all predicates are open.