Provenance in ontology-based data access

We present an approach for dealing with provenance information in an ontology-based data access (OBDA) setting. Our approach is based on provenance semirings, which were studied in database theory as an abstract tool to relate the result of a query with the possible matches of the query in the data. We investigate the problems of (i) deciding whether an ontology annotated with provenance information entails a conjunctive query associated with a provenance polynomial, and (ii) computing a polynomial representing the provenance of a query entailed by a provenance annotated ontology. We show that these polynomials may be infinite in general. We then study a special case where the semiring is idempotent and hence the polynomial is guaranteed to be finite. We instantiate these problems to DL-LiteR and provide some complexity results.