The Sticky Path to Expressive Querying: Decidability of Navigational Queries under Existential Rules

TL;DR

This paper investigates the decidability of regular path queries under various existential rule fragments, showing undecidability for some and decidability for sticky rulesets, thus clarifying the boundaries of query answering in ontology-based systems.

Contribution

It completes the understanding of decidability for RPQ answering across different existential rule fragments, especially highlighting the decidability for sticky rulesets.

Findings

RPQ answering over arbitrary fus rulesets is undecidable.

Decidability is established for sticky rulesets.

A mild extension of RPQ makes the problem undecidable again.

Abstract

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.