From Soft Logic to Hard Rules: A Differentiable Boolean Framework for Interpretable and Balanced Classification

Rule-based models are attractive in domains where decisions must be checked and justified, yet most existing rule learners either rely on discrete search or depend on auxiliary continuous surrogates, making training unstable and difficult to scale on imbalanced data. We propose DiBRL, a differentiable Boolean rule learner that constructs rule sets through stacked logic layers whose operators remain consistent with Boolean semantics before and after discretization. The framework integrates a binarization layer for mixed-type tabular features, differentiable conjunction and disjunction equipped with a margin-based packing mechanism for stable gradient propagation, and an intermediate hardening step that enforces agreement between soft and hard logic. To address class imbalance, DiBRL incorporates the Label-Distribution-Aware Margin (LDAM) loss together with Deferred Re-Weighting (DRW). Experiments on thirteen UCI datasets show that DiBRL performs on par with RRL, LightGBM (LGBM), and XGBoost while keeping the learned rules directly readable. On a real-world acute kidney injury (AKI) prediction task derived from MIMIC-IV, the model achieves competitive AUROC and AUPRC values and produces compact rules that align with clinical patterns, indicating that the learned logic is meaningful for downstream inspection and analysis.