Finite Entailment of UCRPQs over ALC Ontologies

Abstract

We investigate the problem of finite entailment of ontology-mediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCRPQs), extending the well-known class of union of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2ExpTime upper bound for entailment of UCRPQs. At the core of our decision procedure, there is a novel automata-based technique introducing a stratification of interpretations induced by the deterministic finite automaton underlying the input UCRPQ.

Static Analysis of Graph Database Transformations

“…To the best of our knowledge this is the first result on finite containment of C2RPQs in the context of description logics. A related problem of finite entailment has been studied for various logics [27][28][29]31], but while for conjunctive queries the solutions carry over to finite containment, for C(2)RPQs these logics are too weak to allow this. Unrestricted containment of C2RPQs modulo ALCIF TBoxes is known to be in 2EXPTIME [16], but passing from unrestricted to finite structures is typically challenging for such problems.…”

“…Unrestricted containment of C2RPQs modulo ALCIF TBoxes is known to be in 2EXPTIME [16], but passing from unrestricted to finite structures is typically challenging for such problems. For example, finite entailment of CRPQs for a fundamental description logic ALC has been solved only recently [31], 15 years after the unrestricted version [14].…”