Correction to: Checking trustworthiness of probabilistic computations in a typed natural deduction system

In our publication "Checking trustworthiness of probabilistic computations in a typed natural deduction system," Theorem 4.5 and Corollary 4.7 contained an incorrect generalization regarding the preservation of the distance between observed frequencies and theoretical probabilities under term evaluation reductions.Specifically, the original statement incorrectly implied that all considered rule applications preserve this distance.However, adding logical structures (such as pairs or sums) to terms alters the reference variables when computing confidence intervals.This means that, even if the frequency of individual terms lies within the confidence interval relative to their respective reference variables, this does not necessarily hold for their combined term.The issue arises from the shift in reference probability from individual variables (e.g., x and y) to their combined form (e.g., x, y ).Accordingly, we have corrected Theorem 4.5, which now more precisely characterizes the impact of different rule applications.The revised theorem now explicitly states that only the rule I , which makes dependencies on theoretical probabilities explicit, preserves the distance between frequency and theoretical probability.Other rules, such as those introducing new data or constructing complex terms, may affect this distance.Correspondingly, Corollary 4.7 has been adjusted to ref lect this refined result, ensuring that the notion of trustworthiness is preserved only under explicitly identified conditions.These corrections clarify the scope of our claims and ensure consistency with the underlying probabilistic framework.