Answering Conjunctive Queries With Inequalities In Dl-Lite(R)

In the context of the Description Logic DL-Lite(R)(not equal), i.e., DL-Lite(R) without UNA and with inequality axioms, we address the problem of adding to unions of conjunctive queries (UCQs) one of the simplest forms of negation, namely, inequality. It is well known that answering conjunctive queries with unrestricted inequalities over DL-Lite(R) ontologies is in general undecidable. Therefore, we explore two strategies for recovering decidability, and, hopefully, tractability. Firstly, we weaken the ontology language, and consider the variant of DL-Lite(R)(not equal) corresponding to RDFS enriched with both inequality and disjointness axioms. Secondly, we weaken the query language, by preventing inequalities to be applied to existentially quantified variables, thus obtaining the class of queries named UCQ(not equal,b)s. We prove that in the two cases, query answering is decidable, and we provide tight complexity bounds for the problem, both for data and combined complexity. Notably, the results show that answering UCQ(not equal,b)s over DL-Lite(R)(not equal) ontologies is still in AC(0) in data complexity.