On the power of SPARQL in expressing navigational queries

Abstract

Navigational queries on graph databases return binary relations over the nodes of the graph. The calculus of relations, popularized by Tarski, serves as a natural benchmark for first-order navigational querying. Recently, nested regular expressions (nre's) have been proposed to extend navigational querying to resource description framework graphs, i.e. ternary relations. This paper investigates the expressiveness of nre's and their relationship to basic SPARQL queries. An elegant proof is given to the effect that nre queries are already expressible as basic SPARQL queries. This result takes exception of nre's involving Kleene star (transitive closure), but on the other hand it holds even when extending nre's with negation (complementation). The resulting language of ‘star-free nre's with negation (sfnre¬)’ can in fact be captured by a precisely delineated fragment of SPARQL, called Tarski-SPARQL. The resulting language is also compared with an alternative extension that adds negation in the form of the difference operator. While sfnre¬ queries are subsumed by first-order logic with three variables (FO3), it is shown that some natural FO3 queries are not expressible in nre¬, even when allowing transitive closure.