# Why this and not that? A Logic-based Framework for Contrastive Explanations

arXiv: https://arxiv.org/abs/2507.08454 · HTML: https://mlsanity.com/paper/2507.08454/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 11 Jul 2025.

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

- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Model Interpretability through the Lens of Computational Complexity](https://mlsanity.com/paper/2010.12265/) (2020)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [Logic for Explainable AI](https://mlsanity.com/paper/2305.05172/) (2023)
- [Local vs. Global Interpretability: A Computational Complexity Perspective](https://mlsanity.com/paper/2406.02981/) (2024)
- [Explainability via Short Formulas: the Case of Propositional Logic with Implementation](https://mlsanity.com/paper/2209.01403/) (2022)

## Built on by (most cited first, 3 of 3)

- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [Unifying Formal Explanations: A Complexity-Theoretic Perspective](https://mlsanity.com/paper/2602.18160/) (2026)
- [Rethinking Explanations: Formalizing Contrast in Description Logics](https://mlsanity.com/paper/2605.01442/) (2026)

## Abstract (arXiv)

We define several canonical problems related to contrastive explanations, each answering a question of the form ''Why P but not Q?''. The problems compute causes for both P and Q, explicitly comparing their differences. We investigate the basic properties of our definitions in the setting of propositional logic. We show, inter alia, that our framework captures a cardinality-minimal version of existing contrastive explanations in the literature. Furthermore, we provide an extensive analysis of the computational complexities of the problems. We also implement the problems for CNF-formulas using answer set programming and present several examples demonstrating how they work in practice.