Certified Counterfactual Recourse via Goal-Directed Constraint Logic Programming: Inverting Fold-Se Default Rules in High-Stakes Clinical and Financial Domains

Machine learning models deployed in regulated clinical and financial domains must meet rigorous requirements that go beyond raw predictive accuracy: their diagnostic and credit decisions must be intrinsically transparent, deterministic under measurement perturbation, and accompanied by actionable recourse for individuals who receive adverse determinations. Common post-hoc explanation methods, including LIME and SHAP, as well as gradient-based counterfactual optimizers (e.g., Wachter, DiCE), attempt to explain black-box models after training. However, these methods introduce surrogate approximation errors, frequently recommend modifications to immutable physiological or demographic traits (e.g., age, genetic lineage), and fail to provide mathematical validity guarantees. To address these problems, we present an end-to-end neuro-symbolic reasoning framework that bridges forward rule induction and backward constraint verification. The architecture couples FOLD-SE, a scalable first-order default rule learner featuring negation-as-failure (NAF) exception structures, with s(CASP), a goal-directed constraint answer set programming engine that executes without grounding. We evaluated this architecture through strict 10-fold stratified cross-validation on the UCI Dermatology benchmark (366 patient cases, 34 clinical and biopsy features, 6 diagnostic classes) and the German Credit benchmark (1,000 applicants, 61 encoded features, 70/30 class imbalance), the proposed architecture achieves 94.54% accuracy on dermatology and 72.30% on credit risk. Paired Student's t-tests confirm that the accuracy difference relative to deep neural networks is statistically non-significant (dermatology: t(9) = -2.133, p = 0.0617; credit: t(9) = -1.313, p = 0.2218). Importantly, the proposed system achieves 100.0% descriptive fidelity by native derivation and 100.0% actionable counterfactual recourse reachability under immutable trait constraints, compared to 72.6% fidelity and 50.5% reachability for deep neural networks paired with post-hoc surrogates. A multi-criteria TOPSIS analysis across six operational dimensions ranks the proposed pipeline first on both benchmarks (dermatology: 0.9655; credit: 0.9496). Our sensitivity audits confirm that FOLD-SE retains top rank across 100% of weight perturbations on dermatology and 96.7% on credit risk, establishing that explainability and certified recourse do not require compromising predictive power on structured tabular data.