Extensive research in the field of ontology-based query answering has led to the identification of numerous fragments of existential rules (also known as tuple-generating dependencies) that exhibit decidable answering of atomic and conjunctive queries. Motivated by the increased theoretical and practical interest in navigational queries, this paper considers the question for which of these fragments decidability of querying extends to regular path queries (RPQs). In fact, decidability of RPQs has recently been shown to generally hold for the comprehensive family of all fragments that come with the guarantee of universal models being reasonably well-shaped (that is, being of finite cliquewidth). Yet, for the second major family of fragments, known as finite unification sets (short: fus), which are based on first-order-rewritability, corresponding results have been largely elusive so far. We complete the picture by showing that RPQ answering over arbitrary fus rulesets is undecidable. On the positive side, we establish that the problem is decidable for the prominent fus subclass of sticky rulesets, with the caveat that a very mild extension of the RPQ formalism turns the problem undecidable again.

Querying knowledge bases is one of the most important and fundamental tasks in knowledge representation. Although much of the work on querying knowledge bases is focused on conjunctive queries, there is often the need to use a simple form of recursion, such as the one provided by regular path queries (RPQ), which ask for paths defined by a given regular language. Conjunctive RPQs (CRPQs) can then be understood as the generalization of conjunctive queries with this form of recursion. CRPQs are part of SPARQL, the W3C standard for querying RDF data, including well known knowledge bases such as DBpedia and Wikidata. In particular, RPQs are quite popular for querying Wikidata. They are used in over 24% of the queries (and over 38% of the unique queries), according to recent studies (Malyshev et al., 2018; Bonifati et al., 2019). More generally, CRPQs are basic building blocks for querying graph-structured databases (Barceló, 2013). As knowledge bases become larger, reasoning about queries (e.g. for optimization) becomes increasingly important.

We study query answering in the description logic SQ supporting qualified number restrictions on both transitive and non-transitive roles. Our main contributions are a tree-like model property for SQ-knowledge bases and, building upon this, an optimal automata-based algorithm for answering positive existential regular path queries in 2EXPTIME.

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.

Query containment has been studied extensively in KR and databases, for different kinds of query languages and domain constraints. We address the longstanding open problem of containment under expressive description logic (DL) constraints for two-way regular path queries (2RPQs) and their conjunctions, which generalize conjunctive queries with the ability to express regular navigation. We show that, surprisingly, functionality constraints alone make containment of 2RPQs already ExpTime-hard. By employing automata-theoretic techniques, we also provide a matching upper bound that extends to very expressive DL constraints. For conjunctive 2RPQs we prove a further exponential jump in complexity, and provide again a matching upper bound for expressive DLs. Our techniques provide also a solution to the problem of query entailment over DL knowledge bases in which individuals in the ABox may be related through regular role-paths.

A major challenge of query language design is the combination of expressivity with effective static analyses such as query containment. In the setting of XML, documents are seen as finite trees, whose structure may additionally be constrained by type constraints such as those described by an XML schema. We consider the problem of query containment in the presence of type constraints for a class of regular path queries extended with counting and interleaving operators. The counting operator restricts the number of occurrences of children nodes satisfying a given logical property. The interleaving operator provides a succinct notation for describing the absence of order between nodes satisfying a logical property. We provide a logic-based framework supporting these operators, which can be used to solve common query reasoning problems such as satisfiability and containment of queries in exponential time.