A complete classification of the complexity and rewritability of ontology-mediated queries based on the description logic [formula omitted

Abstract

We provide a fine-grained analysis of the data complexity and rewritability of ontology-mediated queries (OMQs) based on an EL ontology and a conjunctive query (CQ). Our main results are that every such OMQ is in ▪, ▪-complete, or ▪-complete and that containment in ▪ coincides with rewritability into linear Datalog (whereas containment in ▪ coincides with rewritability into first-order logic). We establish natural characterizations of the three cases in terms of bounded depth and (un)bounded pathwidth of certain minimal ABoxes on which the OMQ yields an answer. We also show that each of the associated meta problems such as deciding whether a given OMQ is rewritable into linear Datalog is ExpTime-complete. We also give a way to construct linear Datalog rewritings when they exist and prove that there is no constant bound on the arity of IDB relations in linear Datalog rewritings.