# Nondeterministic Causal Models

arXiv: https://arxiv.org/abs/2405.14001 · HTML: https://mlsanity.com/paper/2405.14001/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 11 of 11)

- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Causal Sufficiency and Actual Causation](https://mlsanity.com/paper/2102.02311/) (2021)
- [Probabilistic Reasoning across the Causal Hierarchy](https://mlsanity.com/paper/2001.02889/) (2020)
- [A Causal Analysis of Harm](https://mlsanity.com/paper/2210.05327/) (2022)
- [Quantifying Harm](https://mlsanity.com/paper/2209.15111/) (2022)
- [Reasoning About Causal Models With Infinitely Many Variables](https://mlsanity.com/paper/2112.11362/) (2021)
- [Causal Models with Constraints](https://mlsanity.com/paper/2301.06845/) (2023)
- [Personalised Decision-Making without Counterfactuals](https://mlsanity.com/paper/2301.11976/) (2023)
- [Axiomatizations of causal reasoning under indeterministic causal laws](https://mlsanity.com/paper/2312.07223/) (2023)

## Built on by (most cited first, 2 of 2)

- [Actual Causation and Nondeterministic Causal Models](https://mlsanity.com/paper/2503.07849/) (2025)
- [Robust Counterfactual Policy Optimisation via Nondeterministic Causal Models](https://mlsanity.com/paper/2608.02893/) (2026)

## Abstract (arXiv)

I generalize acyclic deterministic structural causal models to the nondeterministic case and argue that this offers an improved semantics for counterfactuals. The standard, deterministic, semantics developed by Halpern (and based on the initial proposal of Galles & Pearl) assumes that for each assignment of values to parent variables there is a unique assignment to their child variable, and it assumes that the actual world (an assignment of values to all variables of a model) specifies a unique counterfactual world for each intervention. Both assumptions are unrealistic, and therefore I drop both of them in my proposal. I do so by allowing multi-valued functions in the structural equations. In addition, I adjust the semantics so that the solutions to the equations that obtained in the actual world are preserved in any counterfactual world. I provide a sound and complete axiomatization of the resulting logic and compare it to the standard one by Halpern and to more recent proposals that are closer to mine. Finally, I extend these models to the probabilistic case and show that they open up the way to identifying counterfactuals even in Causal Bayesian Networks.