The paper introduces Hybrid-to-NeSy (H2N), a translation framework that recasts hybrid mechanistic/data-driven models as neuro-symbolic interfaces. Mechanistic knowledge is placed on the language side, learned modules on the belief side, and validity domains plus constraints on the logic side. H2N derives an explicit inference functional and two metrics: structural violation rate (SVR), which measures whether learned beliefs respect mechanistic structure, and belief dispersion (BD), interpreted as epistemic uncertainty in the mechanistic component. A noisy binary-classification case study reports that higher SVR and BD are associated with greater held-out accuracy variability. Under structural distribution shift, the metrics quantify uncertainty before accuracy exposes the shift post hoc.
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