Nested Regular Path Queries in Description Logics

TL;DR

This paper investigates the computational complexity of nested regular path queries in description logics, revealing that nesting does not affect data complexity but increases combined complexity in lightweight DLs.

Contribution

It provides tight complexity bounds for nested 2RPQs in various description logics, highlighting the impact of nesting on combined complexity.

Findings

Nesting does not affect data complexity across DLs.

Adding nesting increases combined complexity from P to Exp in lightweight DLs.

Complexity bounds are established for both lightweight and expressive DLs.

Abstract

Two-way regular path queries (2RPQs) have received increased attention recently due to their ability to relate pairs of objects by flexibly navigating graph-structured data. They are present in property paths in SPARQL 1.1, the new standard RDF query language, and in the XML query language XPath. In line with XPath, we consider the extension of 2RPQs with nesting, which allows one to require that objects along a path satisfy complex conditions, in turn expressed through (nested) 2RPQs. We study the computational complexity of answering nested 2RPQs and conjunctions thereof (CN2RPQs) in the presence of domain knowledge expressed in description logics (DLs). We establish tight complexity bounds in data and combined complexity for a variety of DLs, ranging from lightweight DLs (DL-Lite, EL) up to highly expressive ones. Interestingly, we are able to show that adding nesting to (C)2RPQs does not affect worst-case data complexity of query answering for any of the considered DLs. However, in the case of lightweight DLs, adding nesting to 2RPQs leads to a surprising jump in combined complexity, from P-complete to Exp-complete.