Foundations of ontology-based data access under bag semantics

Ontology-based data access (OBDA) is a popular approach for integrating and querying multiple data sources by means of a shared ontology. The ontology is linked to the sources using mappings, which assign to ontology predicates views over the data. The conventional semantics of OBDA is set-based—that is, the extension of the views defined by the mappings does not contain duplicate tuples. This treatment is, however, in disagreement with the standard semantics of database views and database management systems in general, which is based on bags and where duplicate tuples are retained by default. The distinction between set and bag semantics in databases is very significant in practice, and it influences the evaluation of aggregate queries. In this article, we propose and study a bag semantics for OBDA which provides a solid foundation for the future study of aggregate and analytic queries. Our semantics is compatible with both the bag semantics of database views and the set-based conventional semantics of OBDA. Furthermore, it is compatible with existing bag-based semantics for data exchange recently proposed in the literature. We show that adopting a bag semantics makes conjunctive query answering in OBDA coNP-hard in data complexity. To regain tractability of query answering, we consider suitable restrictions along three dimensions, namely, the query language, the ontology language, and the adoption of the unique name assumption. Our investigation shows a complete picture of the computational properties of query answering under bag semantics over ontologies in the DL-Lite family.