From Type to Token: Petri Nets, Individual Token Philosophy, and Individualized Causal Effects

Authors: Fernando Delbianco , Fernando Tohmé , Gustavo Bodanza

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Abstract: Structural Causal Models and Bayesian Networks are the dominant framework for representing causal relations. They are fundamentally type-level formalisms since their estimands, Average Treatment Effects and Conditional Average Treatment Effects, are properties of distributions over populations, not of individual units. When treatment effects exhibit unbounded heterogeneity, these estimands collapse. What persists is the structural, token-level core of causation.

We argue that Petri Nets under the Individual Token Philosophy are the natural representation of these token-level causal structures. We develop a formal translation from Bayesian Networks to Petri Nets, providing a two-layer account of individualized causality. The PN layer provides a structural representation of causal mechanisms that does not rest on distributional assumptions. In turn, a conformal prediction layer quantifies causal effects with finite-sample coverage guarantees. Together they constitute a complete account of individual causal effects.

Subjects:

Artificial Intelligence (cs.AI) ; Machine Learning (stat.ML)

Cite as:

arXiv:2611.05703 [cs.AI]

(or

arXiv:2611.05703v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2611.05703

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arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Fernando Delbianco Dr. [ view email ]

[v1]

Tue, 3 Nov 2026 22:31:10 UTC (22 KB)

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