The Bag Semantics of Ontology-Based Data Access

Abstract

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 views over the data to ontology predicates. Motivated by the need for OBDA systems supporting database-style aggregate queries, we propose a bag semantics for OBDA, where duplicate tuples in the views defined by the mappings are retained, as is the case in standard databases. We show that bag semantics makes conjunctive query answering in OBDA CONP-hard in data complexity. To regain tractability, we consider a rather general class of queries and show its rewritability to a generalisation of the relational calculus to bags.

Fragments of bag relational algebra: Expressiveness and certain answers

“…For the complexity of certain answers, we have a dichotomy: either they can be computed efficiently by naive evaluation, or their complexity is intractable, which means NP-complete, or coNP-complete, or DP-complete (depending on how the problem is turned into a decision problem). Directions for future work are motivated by the recent work on bag semantics in data management applications where incompleteness naturally occurs, such as data exchange [20] and OBDA [28]. Notice that we have primarily concentrated on the closed-world semantics, which as of late has been actively studied in those contexts; see, e.g., [3,5,19,21,27].…”

An ontology-mediated analytics-aware approach to support monitoring and diagnostics of static and streaming data

“…Moreover, for an atomic role P ∈ R, a basic role R, and a data value r ∈ D, interpretation I satisfies: Please note that although the semantics interprets attributes F as bags, extended concepts based on attributes, such as ∃F , are given a classical set-based semantics. This is in contrast to the recent work in [25] that defined bag interpretations as functions assigning to concepts and roles bags over ∆ I and ∆ I × ∆ I , respectively. In the following, we assume the standard name assumption for interpretations I, which requires that individuals and data values are interpreted as themselves, i.e., c I = c for each c ∈ Γ ∪ D. This effectively makes ∆ I and Q equal to Γ and D, respectively.…”

“…In DL-Lite agg A , attributes F are allowed to contain the same tuple multiple times as these duplicates might be produced by the evaluation of the mappings over the database. Retaining these duplicates is crucial for applications that employ aggregation and recent works caring for data aggregation have considered similar settings [25,26].…”

“…In Fig. 1 we present a STARQL query that captures the diagnostic task from our running example and uses concepts, roles, and attributes from our Siemens ontology [19,[21][22][23][24][25]28] and Eq. (1).…”

Querying Attributed DL-Lite Ontologies Using Provenance Semirings

“…The fact that a and b are both married is obtained by combining sources s 1 and s 2 , and by having access to both public and confidential information. Note that using inclusions to propagate annotations allows the query derived from assertions with multiplicities 2 and 3 to have multiplicity 2 × 3, as it would be under the bag semantics (Nikolaou et al 2017).…”