A General Sufficient Condition for Rewriting Horn-ALCHI Atomic Queries into GQL

2026-08-05

AI Summary

This work addresses the problem of efficiently rewriting atomic queries over Horn-ALCHI ontologies into UC2RPQ, a core fragment of the ISO graph query language GQL. To this end, the paper introduces a novel automata-based formal semantics for description logics and incorporates a state stratification condition to eliminate cyclic dependencies. The proposed approach establishes, for the first time, sufficient conditions under which atomic queries over Horn-ALCHI ontologies are rewritable into UC2RPQ. This result substantially extends the applicability of GQL in ontology-mediated querying and provides both a theoretical foundation and a practical pathway for the efficient evaluation of complex ontology-based queries in graph databases.

Abstract

The emergence of the ISO standard GQL introduces a powerful query language extending first-order logic with controlled recursion, raising the question of its applicability to evaluation of ontology-mediated queries (OMQs). We focus on OMQs consisting of atomic queries over ontologies expressed in Horn-ALCHI, an expressive Description Logic that is not, in general, first-order rewritable. To address this, we introduce DL automata, a novel formalism that captures the semantics of such OMQs via runs over fact sets. We then identify a large class of DL automata that can be rewritten into unions of conjunctive two-way regular path queries (UC2RPQs), a central fragment of GQL. Our class of automata relies on a stratification of their states, ruling out specific forms of cyclic dependencies known to raise the complexity. This yields a broad class of Horn-ALCHI OMQs that are GQL-rewritable.

Problem

• ontology-mediated queries
• Horn-ALCHI
• GQL
• query rewriting
• first-order rewritability

Innovation

• DL automata
• GQL rewritability
• Horn-ALCHI
• UC2RPQ
• stratification