# A New Class of Explanations for Classifiers with Non-Binary Features

arXiv: https://arxiv.org/abs/2304.14760 · HTML: https://mlsanity.com/paper/2304.14760/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 68 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 21 of 21)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [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)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Verifying Properties of Binarized Deep Neural Networks](https://mlsanity.com/paper/1709.06662/) (2017)
- [On Explaining Random Forests with SAT](https://mlsanity.com/paper/2105.10278/) (2021)
- [On Tackling Explanation Redundancy in Decision Trees](https://mlsanity.com/paper/2205.09971/) (2022)
- [Explanations for Monotonic Classifiers](https://mlsanity.com/paper/2106.00154/) (2021)
- [On Tractable Representations of Binary Neural Networks](https://mlsanity.com/paper/2004.02082/) (2020)
- [On Validating, Repairing and Refining Heuristic ML Explanations](https://mlsanity.com/paper/1907.02509/) (2019)
- [ASTERYX : A model-Agnostic SaT-basEd appRoach for sYmbolic and score-based eXplanations](https://mlsanity.com/paper/2206.11900/) (2022)
- [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)
- [Computing Abductive Explanations for Boosted Trees](https://mlsanity.com/paper/2209.07740/) (2022)
- [On Quantifying Literals in Boolean Logic and Its Applications to Explainable AI](https://mlsanity.com/paper/2108.09876/) (2021)
- [On Symbolically Encoding the Behavior of Random Forests](https://mlsanity.com/paper/2007.01493/) (2020)
- [On Relating 'Why?' and 'Why Not?' Explanations](https://mlsanity.com/paper/2012.11067/) (2020)
- [A unified logical framework for explanations in classifier systems](https://mlsanity.com/paper/2105.14452/) (2021)
- [Efficient Explanations for Knowledge Compilation Languages](https://mlsanity.com/paper/2107.01654/) (2021)
- [On the Complexity of Enumerating Prime Implicants from Decision-DNNF Circuits](https://mlsanity.com/paper/2301.13328/) (2023)

## Built on by (most cited first, 8 of 8)

- [Delivering Inflated Explanations](https://mlsanity.com/paper/2306.15272/) (2023)
- [Most General Explanations of Tree Ensembles (Extended Version)](https://mlsanity.com/paper/2505.10991/) (2025)
- [Logic-Based Explainability: Past, Present & Future](https://mlsanity.com/paper/2406.11873/) (2024)
- [Circuit Representations of Random Forests with Applications to XAI](https://mlsanity.com/paper/2602.08362/) (2026)
- [Uncovering Bugs in Formal Explainers: A Case Study with PyXAI](https://mlsanity.com/paper/2511.03169/) (2025)
- [Efficient & Correct Predictive Equivalence for Decision Trees](https://mlsanity.com/paper/2509.17774/) (2025)
- [Scaling the Explanation of Multi-Class Bayesian Network Classifiers](https://mlsanity.com/paper/2603.14594/) (2026)
- [Dsat: A Native SAT Solver for Discrete Logic](https://mlsanity.com/paper/2605.09347/) (2026)

## Abstract (arXiv)

Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also an abductive explanation or a PI-explanation. The second type explains why some other decision was not made and is known as a necessary reason for the decision, also a contrastive or counterfactual explanation. These explanations were defined for classifiers with binary, discrete and, in some cases, continuous features. We show that these explanations can be significantly improved in the presence of non-binary features, leading to a new class of explanations that relay more information about decisions and the underlying classifiers. Necessary and sufficient reasons were also shown to be the prime implicates and implicants of the complete reason for a decision, which can be obtained using a quantification operator. We show that our improved notions of necessary and sufficient reasons are also prime implicates and implicants but for an improved notion of complete reason obtained by a new quantification operator that we also define and study.