Bag Semantics of DL-Lite with Functionality Axioms

Abstract

Ontology-based data access (OBDA) is a popular approach for integrating and querying multiple data sources by means of an ontology, which is usually expressed in a description logic (DL) of DL-Lite family. The conventional semantics of OBDA and DLs is set-based—that is, duplicates are disregarded. This disagrees with the standard database bag (multiset) semantics, which is especially important for the correct evaluation of aggregate queries. In this article, we study two variants of bag semantics for query answering over \(\textit{DL-Lite} _{\mathcal{F}}\), extending basic \(\textit{DL-Lite} _{\textit{core}}\) with functional roles. For our first semantics, which follows the semantics of primary keys in SQL, conjunctive query (CQ) answering is coNP-hard in data complexity in general, but it is in TC\(^0\) for the restricted class of rooted CQs; such CQs are also rewritable to the bag relational algebra. For our second semantics, the results are the same except that TC\(^0\) membership and rewritability hold only for the restricted class of ontologies identified by a new notion of functional weak acyclicity.