Abstractions of Queries in Ontology-Based Data Access

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.

Given a knowledge base (KB) with a non-entailed fact, the ABox abduction problem asks for possible extensions of the KB that would entail this fact. This problem has many applications, ranging from diagnosis to explainability and repair. ABox abduction has been well-investigated for consistent KBs and classical semantics, but little is known for the case of inconsistent KBs, which can be caused by erroneous data. In this paper we define suitable notions of abduction in this setting and propose criteria that guide abduction towards "useful" hypotheses. To regain meaningful reasoning in the presence of inconsistencies, we use well-established repair semantics. We provide a comprehensive landscape of the complexity of ABox abduction under repair semantics, treating different variants of the abduction problem for the light-weight description logics DL-Lite and EL_bot.

We study the problem of fitting a description logic (DL) ontology to a given set of positive and negative examples that take the form of an ABox and a Boolean query. While previous work has investigated this problem for the expressive DLs ALC and ALCI, we here focus on the Horn DLs EL and ELI, as well as their extensions with the bottom concept. As the query language, we consider atomic queries (AQs), conjunctive queries (CQs), and unions thereof (UCQs). We provide characterization of the existence of a fitting ontology based on simulations, use them to develop decision procedures, and clarify the exact computational complexity. For AQs, the problem is in PTime for both EL and ELI. For CQs and UCQs, it is $Σ_2^P$-complete for EL and ExpTime-complete for ELI. Adding the bottom concept does not change any of these complexities. Interestingly, moving from ALC and ALCI to EL and ELI introduces additional technical challenges rather than simplifying the matter.