# Rethinking Explanations: Formalizing Contrast in Description Logics

arXiv: https://arxiv.org/abs/2605.01442 · HTML: https://mlsanity.com/paper/2605.01442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 10 of 10)

- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Contrastive Explanation: A Structural-Model Approach](https://mlsanity.com/paper/1811.03163/) (2018)
- [Signature-Based Abduction with Fresh Individuals and Complex Concepts for Description Logics (Extended Version)](https://mlsanity.com/paper/2105.00274/) (2021)
- [Efficient computation of contrastive explanations](https://mlsanity.com/paper/2010.02647/) (2020)
- [Contrastive Explanations for Argumentation-Based Conclusions](https://mlsanity.com/paper/2107.03265/) (2021)
- [Efficient Computation of General Modules for ALC Ontologies (Extended Version)](https://mlsanity.com/paper/2305.09503/) (2023)
- [Why this and not that? A Logic-based Framework for Contrastive Explanations](https://mlsanity.com/paper/2507.08454/) (2025)
- [Why not? Developing ABox Abduction beyond Repairs](https://mlsanity.com/paper/2507.21955/) (2025)
- [Can You Tell the Difference? Contrastive Explanations for ABox Entailments](https://mlsanity.com/paper/2511.11281/) (2025)

## Abstract (arXiv)

There has been a growing interest in explaining entailments over description logic (DL) knowledge bases. The existing explanation formalisms focus on justifications to explain true axioms, and abductive reasoning to explain missing axioms in a knowledge base. However, these formalisms only point out the reasoning steps behind a (missing) entailment and lack a user-centered approach as they do not consider an inquirer's needs, level of understanding, or prior knowledge. We propose contrastive explanations, aiming at answering "why an axiom P (fact) is true instead of another axiom Q (foil)" over description logic knowledge bases. The motivation arises from the observation that when a user discovers that P has occurred, they are often surprised because they anticipated the occurrence of another similar event Q. Furthermore, individual explanations for "why P" and "why not Q" are unsatisfactory since a user expects to see the difference between P and Q. In this work, we first present formal foundations of contrasting questions and then define contrastive explanations within description logics. To this end, facts include ABox assertions of the form C(x) for a concept C and individual x. Possible foils for such facts are assertions C(y) (contrasting against an individual y), or D(x) (contrasting against a concept D). Additionally, we explore the properties of contrastive explanations in the DL EL and ALC. We also provide an implementation of our definition and an experimental evaluation on KBs of varying sizes.