# Beyond Explaining Predictions: Logic-Based Explanations for Confidence in Machine Learning Models

arXiv: https://arxiv.org/abs/2606.10347 · HTML: https://mlsanity.com/paper/2606.10347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [On Validating, Repairing and Refining Heuristic ML Explanations](https://mlsanity.com/paper/1907.02509/) (2019)
- [Computing Abductive Explanations for Boosted Trees](https://mlsanity.com/paper/2209.07740/) (2022)
- [Do Not Trust Additive Explanations](https://mlsanity.com/paper/1903.11420/) (2019)
- [Calibrated Explanations: with Uncertainty Information and Counterfactuals](https://mlsanity.com/paper/2305.02305/) (2023)
- [Delivering Inflated Explanations](https://mlsanity.com/paper/2306.15272/) (2023)
- [Select Wisely and Explain: Active Learning and Probabilistic Local Post-hoc Explainability](https://mlsanity.com/paper/2108.06907/) (2021)
- [Most General Explanations of Tree Ensembles (Extended Version)](https://mlsanity.com/paper/2505.10991/) (2025)
- [FAME: Formal Abstract Minimal Explanation for Neural Networks](https://mlsanity.com/paper/2603.10661/) (2026)
- [Extending XReason: Formal Explanations for Adversarial Detection](https://mlsanity.com/paper/2501.00537/) (2024)
- [Generalizing Logic-based Explanations for Machine Learning Classifiers via Optimization](https://mlsanity.com/paper/2603.01870/) (2026)
- [Concerning Uncertainty -- A Systematic Survey of Uncertainty-Aware XAI](https://mlsanity.com/paper/2603.26838/) (2026)
- [Bound Propagation meets Constraint Simplification: Improving Logic-based XAI for Neural Networks](https://mlsanity.com/paper/2603.01923/) (2026)

## Abstract (arXiv)

Machine learning is increasingly used in critical domains, where both predictions and their associated confidence levels influence important decisions. To enhance transparency in such scenarios, it is important to understand why a model is confident or uncertain about its predictions. Recent logic-based approaches provide abductive explanations, minimal subsets of features sufficient to preserve the predicted class, with correctness guarantees. However, these methods focus solely on classification behavior and may produce explanations that cover instances with low predictive confidence. In this work, we introduce the concept of Minimum Confidence Threshold (MCT), which quantifies the weakest confidence guarantee provided by an abductive explanation. Building upon this concept, we propose confidence-aware abductive explanations, which preserve not only the predicted class but also a user-specified confidence guarantee. We formulate MCT computation as an optimization problem and introduce an algorithm for generating minimal explanations that satisfy a desired confidence threshold. We evaluate the proposed framework on boosted trees for binary classification, although the approach is applicable to other machine learning models that provide confidence scores. Experimental results show that traditional abductive explanations often provide substantially weaker confidence guarantees than the confidence associated with the explained instance itself. In contrast, confidence-aware explanations consistently improve the minimum confidence guaranteed by an explanation while requiring only a modest increase in explanation length. These properties make the proposed approach particularly suitable for applications where both predictive correctness and confidence are essential for trustworthy decision making.