Fitting Horn DL Ontologies to ABox and Query Examples: A Tale of Simulation Quantifiers and Finite Models

2026-04-28

AI Summary

This study addresses the problem of fitting Horn description logic ontologies from positive and negative ABox examples together with Boolean queries, focusing on the fragments EL, ELI, and their extensions with the bottom concept. For atomic queries (AQ), rooted conjunctive queries (CQ), and unions thereof (UCQ), the work introduces simulation relations and finite-model techniques to provide a semantic characterization of the existence of solutions and designs corresponding decision procedures. The main contributions lie in identifying novel challenges arising when moving from ALC to EL and in precisely determining the computational complexity of the fitting problem across query types: it is PTime-complete for AQ; Σ₂^P-complete for rooted CQ and UCQ in EL; and rises to ExpTime-complete in ELI. The inclusion of the bottom concept does not affect these complexity results.

Abstract

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.

Problem

• Horn DL
• ontology fitting
• ABox
• query examples
• description logic

Innovation

• Horn Description Logics
• Ontology Fitting
• Simulation Quantifiers
• Computational Complexity
• Query Learning