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

arXiv: https://arxiv.org/abs/2604.26976 · HTML: https://mlsanity.com/paper/2604.26976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Logical Separability of Labeled Data Examples under Ontologies](https://mlsanity.com/paper/2007.01610/) (2020)
- [The complexity of reverse engineering problems for conjunctive queries](https://mlsanity.com/paper/1606.01206/) (2016)
- [SAT-Based PAC Learning of Description Logic Concepts](https://mlsanity.com/paper/2305.08511/) (2023)
- [Finite Query Answering in Expressive Description Logics with Transitive Roles](https://mlsanity.com/paper/1808.03130/) (2018)
- [Model Theoretic Characterisations of Description Logics](https://mlsanity.com/paper/1305.5820/) (2013)
- [Fitting Description Logic Ontologies to ABox and Query Examples](https://mlsanity.com/paper/2508.08007/) (2025)
- [From Conjunctive Queries to Instance Queries in Ontology-Mediated Querying](https://mlsanity.com/paper/2010.11848/) (2020)
- [Fitting Ontologies and Constraints to Relational Structures](https://mlsanity.com/paper/2508.13176/) (2025)

## Abstract (arXiv)

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 Sigma2P-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.