Actual causality in fault trees: Halpern & Pearl classification

Georgiana Caltais, Milan Lopuhaä‑Zwakenberg and Mariëlle Stoelinga submitted a paper titled "Actual causality in fault trees" to arXiv on 2 Jul 2026 (arXiv:2607.01840; 557 KB). The paper applies Halpern & Pearl's theory of actual causality to fault trees, produces a complete classification of causal notions, and demonstrates how minimal cut sets give rise to actual causes.

What did the authors do?

They produced a complete classification of the different notions of actual causality for fault trees, expressed in terms of the fault tree's graph structure and logical structure. The paper positions fault trees, traditionally a tool to answer "what can go wrong?", as models that can also address "why has it gone wrong?" by mapping Halpern & Pearl causality definitions onto standard fault-tree constructs.

Caltais, Lopuhaä‑Zwakenberg and Stoelinga show how minimal cut set analysis, already central to fault-tree risk assessment, connects to the generation of actual causes under Halpern & Pearl's framework. The authors therefore treat minimal cut sets not only as risk indicators but as structural seeds for causal attribution within the model.

How does Halpern & Pearl's actual causality theory apply to fault trees?

The paper studies fault trees through Halpern & Pearl's theory of actual causality and translates different formal notions of causation into properties of a fault tree's graph and logical composition. The main result is systematic: each variant of actual causality corresponds to identifiable features of the fault tree representation.

In practice, that means the conditions Halpern & Pearl use to judge whether one event is an actual cause of another are checked against the logical gates and connectivity of a fault tree. The authors make these correspondences explicit and classify the causal notions according to both graph-theoretic structure and the logical operators used in the tree.

How do minimal cut sets relate to actual causes?

Minimal cut sets, the minimal combinations of basic failures that cause the top-level system failure, are shown to give rise to actual causes within the Halpern & Pearl perspective. The paper traces how a minimal cut set's logical role in producing the top event translates into the counterfactual and structural conditions that underlie actual causality definitions.

By connecting minimal cut sets to causal attributions, the authors bridge a familiar engineering analysis technique and a formal AI causality theory, allowing fault-tree outputs to be read as candidate causal explanations rather than just risk diagnoses.

Why it matters

Recasting fault trees as instruments that can answer "why has it gone wrong?" shifts their role from descriptive risk models to tools for diagnostic explanation. That matters for failure analysis workflows: diagnostics that rely on structural causes can be made more formal and comparable when mapped to an established causality theory. The paper's explicit classification ties engineering constructs (minimal cut sets, gates, graph layout) to formal semantics for causation, which could reduce ambiguity about what constitutes a cause in system failures.

What to watch

Look for follow-up work that applies the classification to concrete system models or integrates it into diagnostic tools that export fault trees. Also watch for citations of arXiv:2607.01840 and subsequent versions; the authors submitted v1 on 2 Jul 2026 and provided a DOI at https://doi.org/10.48550/arXiv.2607.01840.

References

Paper: "Actual causality in fault trees," Georgiana Caltais, Milan Lopuhaä‑Zwakenberg, Mariëlle Stoelinga, arXiv:2607.01840 (submitted 2 Jul 2026).