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

TL;DR

This paper investigates how to fit Horn description logic ontologies to specific ABox and query examples, providing decision procedures and complexity results for various query types.

Contribution

It characterizes the existence of fitting ontologies using simulations and analyzes the computational complexity for EL and ELI with different query languages.

Findings

For AQs, the problem is in PTime for EL and ELI.

For rooted CQs and UCQ, complexity is Sigma_P^2-complete for EL and ExpTime-complete for ELI.

Adding the bottom concept does not change the 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.