A Horn extension of DL-Lite with NL data complexity

2026-05-13

AI Summary

This work addresses the limited expressiveness of current ontology-mediated query answering (OMQA) systems, which—restricted to DL-Lite—are unable to support NL-complete operations such as path reachability commonly found in graph query languages. To bridge this gap, the authors introduce ELbotpreceq, a Horn description logic that extends the core of DL-Lite by incorporating a stratification mechanism into ELI, thereby harmonizing conjunction and recursion. This logic supports restricted forms of conjunction and reachability axioms and is the first to admit rewriting into fragments of graph query languages, notably nested two-way regular path queries. By doing so, it transcends the traditional dichotomy between AC⁰ and PTime data complexity in OMQA, effectively narrowing the expressivity and complexity gap between ontological reasoning and graph querying, while demonstrating practical utility and expressive power within an NL data complexity bound over a subset of GQL.

Abstract

The literature on ontology-mediated query answering (OMQA) has been shaped by two key results: first-order rewritability for DL-Lite, and PTime-hardness of data complexity for essentially every description logic beyond it. This has effectively positioned DL-Lite as the only practical choice for query rewriting, restricting OMQA solutions to first-order queries and ontologies that can be rewritten into them. This AC0 vs. PTime dichotomy is especially limiting if we consider that OMQA targets graph-structured data, and that standard graph query languages (including the recent ISO standards GQL and SQL/PGQ) are typically NL-complete. Towards identifying a rich Horn DL that can be rewritten into graph query languages and that can still express many ELI and DL-Lite ontologies, we introduce a stratification mechanism for ELI that controls the interaction between conjunction and recursion. In this way, we obtain ELbotpreceq, a description logic that strictly extends the core DL-Lite, supports reachability axioms and restricted conjunction, and allows for reasoning in NL. We establish the NL upper bound via a rewriting into nested two-way regular path queries, a fragment of GQL, providing initial evidence that our ontology language is a promising candidate for extending OMQA to graph query languages.

Problem

• ontology-mediated query answering
• description logic
• graph query languages
• data complexity
• NL-completeness

Innovation

• Horn description logic
• NL data complexity
• ontology-mediated query answering
• graph query languages
• query rewriting