Evaluating Conjunctive and Graph Queries over the EL Profile of OWL 2

Abstract

OWL 2 EL is a popular ontology language that is based on the EL family of description logics and supports regular role inclusions—axioms that can capture compositional properties of roles such as role transitivity and reflexivity. In this thesis, we present several novel complexity results and algorithms for answering expressive queries over OWL 2 EL knowledge bases (KBs) with regular role inclusions. We first focus on the complexity of conjunctive query (CQ) answering in OWL 2 EL and show that the problem is PSpace-complete in combined complexity, the complexity measured in the total size of the input. All the previously known approaches encode the regular role inclusions using finite automata that can be worst-case exponential in size, and thus are not optimal. In our PSpace procedure, we address this problem by using a novel, succinct encoding of regular role inclusions based on pushdown automata with a bounded stack. Moreover, we strengthen the known PSpace lower complexity bound and show that the problem is PSpace-hard even if we consider only the regular role inclusions as part of the input and the query is acyclic; thus, our algorithm is optimal in knowledge base complexity, the complexity measured in the size of the KB, as well as for acyclic queries. We then study graph queries for OWL 2 EL and show that answering positive, converse-free conjunctive graph queries is PSpace-complete. Thus, from a theoretical perspective, we can add navigational features to CQs over OWL 2 EL without an increase in complexity. Finally, we present a practicable algorithm for answering CQs over OWL 2 EL KBs with only transitive and reflexive composite roles. None of the previously known approaches target transitive and reflexive roles specifically, and so they all run in PSpace and do not provide a tight upper complexity bound. In contrast, our algorithm is optimal: it runs in NP in combined complexity and in PTime in KB complexity. We also show that answering CQs is NP-hard in combined complexity if the query is acyclic and the KB contains one transitive role, one reflexive role, or nominals—concepts containing precisely one individual.