Ontology-Mediated Querying with the Description Logic EL: Trichotomy and Linear Datalog Rewritability

We consider ontology-mediated queries (OMQs) based on an EL ontology and an atomic query (AQ), provide an ultimately fine-grained analysis of data complexity and study rewritability into linear Datalog-aiming to capture linear recursion in SQL. Our main results are that every such OMQ is in AC(0), NL-complete or PTIME-complete, and that containment in NL coincides with rewritability into linear Datalog (whereas containment in AC(0) coincides with rewritability into first-order logic). We establish natural characterizations of the three cases, show that deciding linear Datalog rewritability (as well as the mentioned complexities) is EXPTIME-complete, 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.