Answering Path Queries under Linear and Guarded Existential Rules

2026-06-22

Journal of Artificial Intelligence Research

AI Summary

This study addresses the unresolved computational complexity of ontology-mediated two-way regular path queries under linear and guarded existential rules. By employing complexity theory, reduction techniques, and rigorous mathematical proofs integrated with ontological reasoning, it systematically evaluates performance boundaries across diverse scenarios. The primary contribution is the first demonstration that, under guarded rules, path queries exhibit the same complexity as conjunctive queries. Furthermore, it establishes that the data complexity under linear rules matches that of pure graph databases. Ultimately, this work precisely delineates the complexity landscape: query evaluation under linear rules is NL-complete, while under guarded rules, the data complexity is PTime-complete and the combined complexity is 2ExpTime-complete.

Abstract

Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries (CQs), navigational queries have gained increasing attention. In this paper, we investigate the complexity of answering two-way (conjunctive) regular path queries ((C)RPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that (C)RPQ answering is NL-complete in data complexity, which matches the data complexity of answering RPQs over plain graph databases (i.e., without an ontology). In combined complexity, both tasks are ExpTime-complete in the general case, but RPQ and CRPQ answering drop to PTime-complete and PSpace-complete respectively if there is a bound on predicate arity. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of (C)RPQ answering is the same as for CQs, namely 2ExpTime-complete in combined complexity (ExpTime-complete in the bounded-arity case) and PTime-complete in data complexity.

Problem

• Ontology-mediated query answering
• Regular path queries
• Guarded existential rules
• Linear existential rules
• Computational complexity

Innovation

• Ontology-mediated query answering
• Regular path queries
• Guarded existential rules
• Computational complexity
• Linear existential rules