Fitting Horn DL Ontologies to ABox and Query Examples: A Tale of Simulation Quantifiers and Finite Models
For researchers in description logic and ontology learning, this work provides the first complexity analysis for fitting Horn DL ontologies to examples, revealing that the problem is harder than for expressive DLs.
The paper characterizes the existence of a fitting Horn DL ontology (EL/ELI) to ABox and query examples, providing decision procedures and complexity results: PTime for AQs, Σ_P^2-complete for rooted CQs/UCQs in EL, and ExpTime-complete in ELI.
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 (rooted CQs), and unions thereof (rooted 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 rooted CQs and UCQ, it is Sigma_P^2-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.