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

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.

Local conformal prediction for individual causal effects
Fernando Delbianco, Fernando Tohme
arXiv20 Oct 2026PreprintCC BY 4.0Full textStatisticsarXiv
lepidoptera: A Domain-Agnostic Engine for Causal Simulation with Mixed Variable Types, Vine Copula Dependence, and Individual-Level Counterfactual Propagation
Danilo Augusto Sarti
arXiv16 Oct 2026PreprintCC BY 4.0Full textStatisticsarXiv
Mixed-effects two-stage residual inclusion methods for individual patient data meta-analysis: A methodological framework for causal inference in survival analysis
Heather Hufstedler, Alexander M. Danzer, Valentijn Marnix Theodoor de Jong +1
Research Synthesis Methods29 Jun 2026Peer-reviewedCC BY 4.0Full textStatisticsPMC
Universal Properties of Petri Net Unfoldings
Serge Lechenne, Hugo Paquet
arXiv15 Sep 2026PreprintCC BY 4.0Full textAlgebra & number theoryarXiv
Group Petri Nets: Structural and Algebraic Models for Finite Groups and Their Subgroups
Girish K P
HAL1 Nov 2026PreprintCC BY-NC-ND 4.0Full textGeneral mathematicsHAL

Cite

BibTeX RIS

BibTeX

@misc{delbianco2026from,
  title = {{From Type to Token: Petri Nets, Individual Token Philosophy, and Individualized Causal Effects}},
  author = {Fernando Delbianco and Fernando Tohmé and Gustavo Bodanza},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05703},
  eprint = {2611.05703},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05703},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - From Type to Token: Petri Nets, Individual Token Philosophy, and Individualized Causal Effects
AU  - Fernando Delbianco
AU  - Fernando Tohmé
AU  - Gustavo Bodanza
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05703
UR  - https://arxiv.org/abs/2611.05703
AB  - 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.
ER  -

Abstract

Related

Cite