Yazmin Angélica Ibáñez-García

Conjunctive queries with negation over DL-Lite: a closer look

While conjunctive query (CQ) answering over DL-Lite has been studied extensively, there have been few attempts to analyse CQs with negated atoms. This paper deepens the study of the problem. Answering CQs with safe negation and CQs with a single inequality over DL-Lite with role inclusions is shown to be undecidable, even for a fixed TBox and query.Without role inclusions, answering CQs with one inequality is P-hard and with two inequalities coNP-hard in data complexity.

An update on query answering with restricted forms of negation

One of the most prominent applications of description logic ontologies is their use for accessing data. In this setting, ontologies provide an abstract conceptual layer of the data schema, and queries over the ontology are then used to access the data. In this paper we focus on extensions of conjunctive queries (CQs) and unions of conjunctive queries (UCQs) with restricted forms of negations such as inequality and safe negation. In particular, we consider ontologies based on members of the DL-Lite family. We show that by extending UCQs with any form of negated atoms, the problem of query answering becomes undecidable even when considering ontologies expressed in the core fragment of DL-Lite. On the other hand, we show that answering CQs with inequalities is decidable for ontologies expressed in DL-

Query Answering with DBoxes is Hard

Lite^{\mathcal{H}}_{core}

Queries with negation and inequalities over lightweight ontologies

. To this end, we provide an algorithm matching the known coNP lower bound on data complexity. Furthermore, we identify a setting in which conjunctive query answering with inequalities is tractable. We regain tractability by means of syntactic restrictions on the queries, but keeping the expressiveness of the ontology.