The Bag Semantics of Ontology-Based Data
           Access (Extended Abstract)?

     Charalampos Nikolaou, Egor V. Kostylev, George Konstantinidis, Mark
             Kaminski, Bernardo Cuenca Grau, and Ian Horrocks

              Department of Computer Science, University of Oxford, UK

    Ontology-based data access (OBDA) is an increasingly popular approach
to enable uniform access to multiple data sources with diverging schemas. In
OBDA, an ontology provides a unifying conceptual model for the data sources
together with domain knowledge. The ontology is linked to each source by global-
as-view (GAV) mappings, which assign views over the data to ontology predi-
cates. Users access the data by means of queries formulated using the vocabulary
of the ontology; query answering amounts to computing the certain answers of
the query over the union of ontology and the materialisation of the views defined
by the mappings. The formalism of choice for representing ontologies in OBDA
is the description logic DL-LiteR which underpins OWL 2 QL. DL-LiteR was
designed to ensure that queries against the ontology are first-order rewritable;
that is, they can be reformulated as a set of relational queries over the sources.
    An important observation about the conventional semantics of OBDA is that
it is set-based: the materialisation of the views defined by the mappings is for-
malised as a virtual ABox consisting of a set of facts over the ontology predi-
cates. This treatment is, however, in disagreement with the semantics of database
views, which is based on bags (multisets) and where duplicate tuples are retained
by default. The distinction between set and bag semantics in databases is very
important in practice since it influences the evaluation of aggregate queries that
combine various aggregation functions (e.g., Min, Max, Sum, Count, Avg) with
the grouping functionality provided in SQL by the GroupBy construct.
    In this paper we study a bag semantics for OBDA that is compatible with
the semantics of standard databases and can provide the foundations for the
future study of aggregate queries. We propose the ontology language DL-Litebag     R
and its restriction DL-Litebag
                             core , where ABoxes consist of a bag of facts. We define
the bag semantics of conjunctive query (CQ) answering and show that it is com-
patible with the conventional set semantics. However, we show that DL-Litebag     core
ontologies may not admit a universal model while CQ answering becomes coNP-
hard in data complexity, hence losing first-order rewritability of CQs. To regain
tractability, we study the class of rooted CQs, which captures most practical
OBDA queries, and show that it admits universal models and enjoys first-order
rewritability for DL-Litebag
                           core ontologies. Unfortunately, these properties do not
extend to DL-LitebagR where CQ answering remains coNP-hard.

?
    This is the extended abstract of the paper accepted for publication in the proceedings
    of IJCAI 2017. The full paper may be accessed at arXiv:1705.07105 [cs.AI]. Work
    supported by the Royal Society under a University Research Fellowship, the EPSRC
    projects ED3 and DBOnto, and the Research Council of Norway via the Sirius SFI.