Containment in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics

We study query containment in three closely related formalisms: monadic disjunctive Datalog (MDDLog), MMSNP (a logical generalization of constraint satisfaction problems), and ontology-mediated queries (OMQs) based on expressive description logics and unions of conjunctive queries. Containment in MMSNP was known to be decidable due to a result by Feder and Vardi, but its exact complexity has remained open. We prove 2NExpTime-completeness and extend this result to monadic disjunctive Datalog and to OMQs.