Efficient Counterfactual Reasoning in ProbLog via Single World Intervention Programs

Saimun Habib; Vaishak Belle; Fengxiang He

cs.AIMar 20, 2026

Efficient Counterfactual Reasoning in ProbLog via Single World Intervention Programs

Authors: Saimun Habib, Vaishak Belle, Fengxiang He

Organizations: University of Edinburgh, Edinburgh, United Kingdom · The MITRE Corporation, McLean, Virgina, USA

Abstract

Probabilistic Logic Programming (PLP) languages, like ProbLog, naturally support reasoning under uncertainty, while maintaining a declarative and interpretable framework. Meanwhile, counterfactual reasoning (i.e., answering ``what if'' questions) is critical for ensuring AI systems are robust and trustworthy; however, integrating this capability into PLP can be computationally prohibitive and unstable in accuracy. This paper addresses this challenge, by proposing an efficient program transformation for counterfactuals as Single World Intervention Programs (SWIPs) in ProbLog. By systematically splitting ProbLog clauses to observed and fixed components relevant to a counterfactual, we create a transformed program that (1) does not asymptotically exceed the computational complexity of existing methods, and is strictly smaller in common cases, and (2) reduces counterfactual reasoning to marginal inference over a simpler program. We formally prove the correctness of our approach, which relies on a weaker set independence assumptions and is consistent with conditional independencies, showing the resulting marginal probabilities match the counterfactual distributions of the underlying Structural Causal Model in wide domains. Our method achieves a 35% reduction in inference time versus existing methods in extensive experiments. This work makes complex counterfactual reasoning more computationally tractable and reliable, providing a crucial step towards developing more robust and explainable AI systems. The code is at https://github.com/EVIEHub/swip.

Figures & tables

Panel of Figure 1 — Figure 1: A causal diagram with variables $L$ , $D$ , $G$ , and $H$ . The corresponding SCM declares $H$ as a function of $A$ , $B$ and $C$ , $D$ as a function of $G$ and $L$ , and $L$ as functions of $G$ .

Panel of Figure 2 — Figure 2: Side-by-side comparison of (a) the original structural causal model and (b) its corresponding twin network construction.

Panel of Figure 3 — Figure 3: SWIG where intervention $fix(L=l)$ is acted

Panel of Figure 4 — Figure 4: Construction of benchmark DAGs. A random tree of size $n$ rooted at $s$ (top) is generated, a dense layer of $k$ nodes $u_{1},\dots,u_{k}$ is added below (each receiving edges from multiple tree nodes), and a single goal node $g$ is appended below the dense layer receiving edges from every $u_{i}$ .

Figure 5: Unfolded treewidth as a function of synthetic graph size and original treewidth. The SWIG-based transformation yields narrower unfolded dependency structures than the Twin Network approach.

Figure 6: Mean compilation and inference times for varying numbers of evidence and intervention atoms. The SWIG-based transformation achieves lower inference and compilation times, corresponding to its smaller unfolded program structures.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Definition
$\mathbf{V}$	Set of endogenous variables
$\mathbf{U}$	Set of exogenous variables
$\mathcal{F}$	Set of functional equations
$pa(X)$	Set of endogenous parents of $x$
$\mathcal{M}$	Structural causal model (SCM): tuple of $\langle\textbf{U},\textbf{V},\mathcal{F}\rangle$
$X:=f_{X}(\mathrm{pa}(X),\epsilon_{X})$	Structural equation for variable $X$ w

Appendix

Table 1: Summary of key notation used throughout the paper.

\pi^{l}(\phi):=\begin{cases}1,&\mathcal{I}(l)\models(E=e)\;\wedge\;\mathcal{P}^{\sigma(l),do(X:=x)}\models\phi\\ 0,&\text{else}.\end{cases}

Appendix

Algorithm 5 Treatment of Counterfactuals in CP-logic

\pi^{l}(\phi):=\begin{cases}1,&\mathcal{I}(l)\models(E=e)\;\wedge\;\mathcal{P}^{\sigma(l),fix(X:=x)}\models\phi\\ 0,&\text{else}.\end{cases}

Appendix

Algorithm 6 Fixed Operator Counterfactuals in CP-logic

Counterfactual Reasoning

Counterfactual reasoning studies how outcomes would change under alternative actions, events, or conditions.

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Jun 18, 2026J/K move · Enter open · S save

DeepSWIP: Quotient-WMC Counterfactuals for Neural Probabilistic Logic Programs

Saimun Habib, Vaishak Belle, Fengxiang He

University of Edinburgh

Probabilistic Logic Structural Causal Models Neuro-Symbolic Reasoning Probabilistic Programming Counterfactual Reasoning

Open paper AskPDF arXiv

Neurosymbolic systems such as DeepProbLog combine neural perception with probabilistic logic, but standard inference is associational. Counterfactual reasoning additionally requires a causal semantics for interventions and evidence. We introduce DeepSWIP, a single-world counterfactual semantics for DeepProbLog programs. Using neural materialization, we reduce fixed-context neural predicates to ordinary ProbLog choices, apply Single World Intervention Programs (SWIPs), and compute counterfactuals by weighted model counting (WMC) over a single transformed program. Under finite grounding and unique-supported-model assumptions, DeepSWIP is exact relative to the learned materialized FCM. The standard quotient-WMC form of ProbLog conditionals identifies active neural probabilities and explains intervention cleaning, calibration sensitivity, and rare-evidence instability. Experiments on MPI3D confirm the transformation against a DeepTwin construction against 12,000 queries, as predicted and a 2.14

\times

inference speedup from avoiding the Twin's endogenous duplication. A SUMO HOV experiment shows that neural calibration degradation biases plug-in estimates, while a correctly scoped randomized-policy AIPW estimator removes most first-order bias for population mean and ATE estimands. Code is at https://github.com/saibib/deep_SWIP.

Abstract

Counterfactual Reasoning

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