Conjunctive regular path queries are an expressive extension of the well-known class of conjunctive queries. Such queries have been extensively studied in the (graph) database community, since they support a controlled form of recursion and enable sophisticated path navigation. Somewhat surprisingly, there has been little work aimed at using such queries in the context of description logic (DL) knowledge bases, particularly for the lightweight DLs that are considered best suited for data-intensive applications. This paper aims to bridge this gap by providing algorithms and tight complexity bounds for answering two-way conjunctive regular path queries over DL knowledge bases formulated in lightweight DLs of the DL-Lite and EL families. Our results demonstrate that in data complexity, the cost of moving to this richer query language is as low as one could wish for: the problem is NL-complete for DL-Lite and P-complete for EL. The combined complexity of query answering increases from NP- to PSpace-complete, but for two-way regular path queries (without conjunction), we show that query answering is tractable even with respect to combined complexity. Our results reveal two-way conjunctive regular path queries as a promising language for querying data enriched by ontologies formulated in DLs of the DL-Lite and EL families or the corresponding OWL 2 QL and EL profiles.
In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations.
SPARQL entailment regimes are strongly influenced by the big body of works on ontology-based query answering, notably in the area of Description Logics (DLs). However, the semantics of query answering under SPARQL entailment regimes is defined in a more naive and much less expressive way than the certain answer semantics usually adopted in DLs. The goal of this work is to introduce an intuitive certain answer semantics also for SPARQL and to show the feasibility of this approach. For OWL 2 QL entailment, we present algorithms for the evaluation of an interesting fragment of SPARQL (the so-called well-designed SPARQL). Moreover, we show that the complexity of the most fundamental query analysis tasks (such as query containment and equivalence testing) is not negatively affected by the presence of OWL 2 QL entailment under the proposed semantics.
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