Regular Path Queries in Lightweight Description Logics: Complexity and Algorithms

Abstract

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.

On the Complexity of Evaluating Regular Path Queries over Linear Existential Rules

“…We consider the problem of computing the certain answers to a regular path query and show how to adapt the construction in [5] to the case of linear rules. There are two main ingredients in the original algorithm for DL-Lite:…”

“…To take care of the first difficulty, we utilize a finer notion of type, which has similar properties to the one used in [5].…”

“…We can overcome the second difficulty by generalizing the Loop table introduced in [5], which keeps track of the paths that occur 'below' a given type. Intuitively, a type T is in the cell indexed by (s i , j, s i , j ) if and only if below any atom of type T , there is a path going from the term in position j to the term in position j labeled by a word that takes A from state s i to state s i .…”

“…In recent years, the problem of answering navigational queries in the setting of OMQA has begun to be explored, first for ontologies formulated in highly expressive description logics (DLs) of the Z family [8,9,10], then for rich Horn DLs like Horn-SROIQ [18], and more recently, for lightweight DLs like DL-Lite R and EL [19,5]. The latter DLs, which underlie the OWL 2 QL and EL profiles, are the most relevant for OMQA due to their favourable computational properties.…”

“…After introducing the necessary background, we show how to adapt the RPQ algorithm for DL-Lite proposed in [5] to the setting of linear rules. Unfortunately, our adaptation incurs an exponential blow-up with respect to the maximum predicate arity.…”