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

When answering queries in the presence of ontologies, adopting the closed world assumption for some predicates easily results in intractability. We analyze this situation on the level of individual ontologies formulated in the description logics DLLite and EL and show that in all cases where answering conjunctive queries (CQs) with (open and) closed predicates is tractable, it coincides with answering CQs with all predicates assumed open. In this sense, CQ answering with closed predicates is inherently intractable. Our analysis also yields a dichotomy between AC and CONP for CQ answering w.r.t. ontologies formulated in DL-Lite and a dichotomy between PTIME and CONP for EL. Interestingly, 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.