# On Relating 'Why?' and 'Why Not?' Explanations

arXiv: https://arxiv.org/abs/2012.11067 · HTML: https://mlsanity.com/paper/2012.11067/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2020.

## Built on by (most cited first, 15 of 15)

- [Explanations for Monotonic Classifiers](https://mlsanity.com/paper/2106.00154/) (2021)
- [ASTERYX : A model-Agnostic SaT-basEd appRoach for sYmbolic and score-based eXplanations](https://mlsanity.com/paper/2206.11900/) (2022)
- [Computing Abductive Explanations for Boosted Trees](https://mlsanity.com/paper/2209.07740/) (2022)
- [A New Class of Explanations for Classifiers with Non-Binary Features](https://mlsanity.com/paper/2304.14760/) (2023)
- [On the Explanatory Power of Decision Trees](https://mlsanity.com/paper/2108.05266/) (2021)
- [On the Complexity of Enumerating Prime Implicants from Decision-DNNF Circuits](https://mlsanity.com/paper/2301.13328/) (2023)
- [Sufficient, Necessary and Complete Causal Explanations in Image Classification](https://mlsanity.com/paper/2507.23497/) (2025)
- [Abductive and Contrastive Explanations for Scoring Rules in Voting](https://mlsanity.com/paper/2408.12927/) (2024)
- [Explaining Tournament Solutions with Minimal Supports](https://mlsanity.com/paper/2509.09312/) (2025)
- [Finding Counterfactual Explanations through Constraint Relaxations](https://mlsanity.com/paper/2204.03429/) (2022)
- [CLIMAX: An exploration of Classifier-Based Contrastive Explanations](https://mlsanity.com/paper/2307.00680/) (2023)
- [Rectifying Mono-Label Boolean Classifiers](https://mlsanity.com/paper/2206.08758/) (2022)
- [A Model-Agnostic SAT-based Approach for Symbolic Explanation Enumeration](https://mlsanity.com/paper/2206.11539/) (2022)
- [Ranking Counterfactual Explanations](https://mlsanity.com/paper/2503.15817/) (2025)
- [Leveraging Association Rules for Better Predictions and Better Explanations](https://mlsanity.com/paper/2510.18628/) (2025)

## Abstract (arXiv)

Explanations of Machine Learning (ML) models often address a 'Why?' question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that address a 'Why Not?' question, i.e. finding a change of feature values that guarantee a change of prediction. Given their goals, these two forms of explaining predictions of ML models appear to be mostly unrelated. However, this paper demonstrates otherwise, and establishes a rigorous formal relationship between 'Why?' and 'Why Not?' explanations. Concretely, the paper proves that, for any given instance, 'Why?' explanations are minimal hitting sets of 'Why Not?' explanations and vice-versa. Furthermore, the paper devises novel algorithms for extracting and enumerating both forms of explanations.