# A Formal Approach to Explainability

arXiv: https://arxiv.org/abs/2001.05207 · HTML: https://mlsanity.com/paper/2001.05207/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2020.

## Built on by (most cited first, 9 of 9)

- [Framework for Evaluating Faithfulness of Local Explanations](https://mlsanity.com/paper/2202.00734/) (2022)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [On Tackling Explanation Redundancy in Decision Trees](https://mlsanity.com/paper/2205.09971/) (2022)
- [Zorro: Valid, Sparse, and Stable Explanations in Graph Neural Networks](https://mlsanity.com/paper/2105.08621/) (2021)
- [On Computing Probabilistic Abductive Explanations](https://mlsanity.com/paper/2212.05990/) (2022)
- [Mitigating Covertly Unsafe Text within Natural Language Systems](https://mlsanity.com/paper/2210.09306/) (2022)
- [Auditing Local Explanations is Hard](https://mlsanity.com/paper/2407.13281/) (2024)
- [Formal Abductive Latent Explanations for Prototype-Based Networks](https://mlsanity.com/paper/2511.16588/) (2025)
- [Improving the Validity of Decision Trees as Explanations](https://mlsanity.com/paper/2306.06777/) (2023)

## Abstract (arXiv)

We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these properties and between explanation-generating functions and intermediate representations of learned models and are able to show, for example, that if the activations of a given layer are consistent with an explanation, then so do all other subsequent layers. In addition, we study the intersection and union of explanations as a way to construct new explanations.