# On The Reasons Behind Decisions

arXiv: https://arxiv.org/abs/2002.09284 · HTML: https://mlsanity.com/paper/2002.09284/

## Key facts

- Cited by 100 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2020.

## Built on by (most cited first, 30 of 100)

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- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [On Tackling Explanation Redundancy in Decision Trees](https://mlsanity.com/paper/2205.09971/) (2022)
- [On the Computational Intelligibility of Boolean Classifiers](https://mlsanity.com/paper/2104.06172/) (2021)
- [SAT-Based Rigorous Explanations for Decision Lists](https://mlsanity.com/paper/2105.06782/) (2021)
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- [Trading Complexity for Sparsity in Random Forest Explanations](https://mlsanity.com/paper/2108.05276/) (2021)
- [Provably efficient, succinct, and precise explanations](https://mlsanity.com/paper/2111.01576/) (2021)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [Interpretable Data-Based Explanations for Fairness Debugging](https://mlsanity.com/paper/2112.09745/) (2021)
- [Causal Explanations and XAI](https://mlsanity.com/paper/2201.13169/) (2022)
- [VeriX: Towards Verified Explainability of Deep Neural Networks](https://mlsanity.com/paper/2212.01051/) (2022)
- [Foundations of Symbolic Languages for Model Interpretability](https://mlsanity.com/paper/2110.02376/) (2021)
- [Probabilistic Sufficient Explanations](https://mlsanity.com/paper/2105.10118/) (2021)
- [On the Computation of Necessary and Sufficient Explanations](https://mlsanity.com/paper/2203.10451/) (2022)
- [Eliminating The Impossible, Whatever Remains Must Be True](https://mlsanity.com/paper/2206.09551/) (2022)
- [Computing Abductive Explanations for Boosted Trees](https://mlsanity.com/paper/2209.07740/) (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)
- [On Computing Probabilistic Abductive Explanations](https://mlsanity.com/paper/2212.05990/) (2022)
- [SpArX: Sparse Argumentative Explanations for Neural Networks [Technical Report]](https://mlsanity.com/paper/2301.09559/) (2023)
- [On Quantifying Literals in Boolean Logic and Its Applications to Explainable AI](https://mlsanity.com/paper/2108.09876/) (2021)
- [A unified logical framework for explanations in classifier systems](https://mlsanity.com/paper/2105.14452/) (2021)
- [Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations](https://mlsanity.com/paper/2506.08505/) (2025)
- [Efficient Explanations With Relevant Sets](https://mlsanity.com/paper/2106.00546/) (2021)

## Abstract (arXiv)

Recent work has shown that some common machine learning classifiers can be compiled into Boolean circuits that have the same input-output behavior. We present a theory for unveiling the reasons behind the decisions made by Boolean classifiers and study some of its theoretical and practical implications. We define notions such as sufficient, necessary and complete reasons behind decisions, in addition to classifier and decision bias. We show how these notions can be used to evaluate counterfactual statements such as "a decision will stick even if ... because ... ." We present efficient algorithms for computing these notions, which are based on new advances on tractable Boolean circuits, and illustrate them using a case study.