A Framework for Explaining Query Answers in DL-Lite

An Ontology-based Data Access system is constituted by an ontology, namely a description of the concepts and the relations in a domain of interest, a database storing facts about the domain, and a mapping between the data and the ontology. In this paper, we consider ontologies expressed in the popular DL-Lite family of Description Logic, and we address the problem of computing explanations for answers to queries in an OBDA system, where queries are either positive, in particular conjunctive queries, or negative, i.e., negation of conjunctive queries. We provide the following contributions: (i) we propose a formal, comprehensive framework of explaining query answers in OBDA systems based on DL-Lite; (ii) we present an algorithm that, given a tuple returned as an answer to a positive query, and given a weighting function, examines all the explanations of the answer, and chooses the best explanation according to such function; (iii) we do the same for the answers to negative queries. Notably, on the way to get the latter result, we present what appears to be the first algorithm that computes the answers to negative queries in DL-Lite.