DeepSWIP: Single-World Counterfactual Semantics for DeepProbLog

Counterfactual answers in machine learning are trustworthy only relative to an explicit account of mechanisms, interventions, and the units over which alternatives are compared. This paper gives such an account for DeepProbLog-style neuro-symbolic programs. DeepSWIP first materializes neural predicates as probabilistic choices, inducing a structural causal model whose endogenous assignments are the logical rules. It then applies a Single World Intervention Program transformation so clauses defining intervened atoms are removed, fixed intervention atoms are inserted, and counterfactual inference is reduced to ordinary weighted model counting in the transformed program. The resulting semantics is single-world in the sense of Richardson and Robins' SWIGs where it represents the relevant potential-outcome world without duplicating the entire endogenous program. This is particularly natural for neural predicates, since a learned classifier or perception module is a parameterized measurement mechanism, not a separate copy of itself in each hypothetical world. We distinguish the exactness of the symbolic transformation from statistical identification and calibration; cross-fitting can reduce plug-in bias in learned nuisance components, but it does not by itself identify counterfactuals in observational settings. The contribution is a precise bridge between SCMs, potential-outcome notation, and neuro-symbolic weighted model counting.