A Horn extension of DL-Lite with NL data complexity

TL;DR

This paper introduces ELbotpreceq, a Horn extension of DL-Lite, enabling NL data complexity and rewriting into graph query languages, thus broadening practical ontology-mediated query answering capabilities.

Contribution

It proposes a new description logic extending DL-Lite with NL reasoning and graph query rewritability, addressing limitations of existing OMQA approaches.

Findings

ELbotpreceq supports reachability axioms and restricted conjunction.

Reasoning in ELbotpreceq is in NL due to a rewriting into nested two-way regular path queries.

The logic extends DL-Lite and can be rewritten into GQL fragment.

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.