Containment for Rule-Based Ontology-Mediated Queries
This work addresses static analysis tasks for OMQs, which is incremental as it builds on existing formalisms to provide complexity results for containment.
The paper tackled the containment problem for ontology-mediated queries (OMQs) expressed under guarded, non-recursive, and sticky sets of tuple-generating dependencies, developing tailored techniques to obtain sharp complexity bounds and applying them to related problems like distribution over components and UCQ rewritability.
Many efforts have been dedicated to identifying restrictions on ontologies expressed as tuple-generating dependencies (tgds), a.k.a. existential rules, that lead to the decidability for the problem of answering ontology-mediated queries (OMQs). This has given rise to three families of formalisms: guarded, non-recursive, and sticky sets of tgds. In this work, we study the containment problem for OMQs expressed in such formalisms, which is a key ingredient for solving static analysis tasks associated with them. Our main contribution is the development of specially tailored techniques for OMQ containment under the classes of tgds stated above. This enables us to obtain sharp complexity bounds for the problems at hand, which in turn allow us to delimitate its practical applicability. We also apply our techniques to pinpoint the complexity of problems associated with two emerging applications of OMQ containment: distribution over components and UCQ rewritability of OMQs.