Belief Ledgers: Posterior Accounting for Auditable, Faithful Explanations

Reliable explanations for evidence-driven NLP systems should reflect how a prediction is formed, not merely identify plausible evidence. We introduce **Belief Ledgers**, a probabilistic framework that turns retrieved passages, extracted claims, and numerical comparisons into an auditable sequence of posterior updates. Belief Ledgers group dependent evidence into clusters, compute cluster-level log Bayes factors for binary decisions, and use a separate conjugate Gaussian model for continuous margins, ensuring that all displayed contributions remain in a consistent accounting space. The resulting explanation contains provenance-linked evidence entries that exactly sum to the model’s posterior log-odds and supports controlled counterfactual interventions. Across scientific claim verification, multi-sentence reading comprehension, and fact verification, Belief Ledgers improve predictive performance while substantially improving calibration. On SciProp, they achieve 75.8% accuracy and 0.034 ECE, versus 74.2% and 0.120 ECE for a strong NLI-aggregation baseline. Matched deletion/insertion tests and ablations further show that ledger-ranked evidence is causally predictive of model confidence and that dependence-aware clustering is critical. Belief Ledgers offer a practical path to calibrated, testable explanations for evidence-aggregation pipelines.