Nondeterministic Causal Models

TL;DR

This paper extends deterministic causal models to nondeterministic ones using multi-valued functions, improving counterfactual semantics and enabling probabilistic reasoning in causal networks.

Contribution

It introduces a nondeterministic framework for structural causal models with multi-valued functions, enhancing counterfactual analysis and extending to probabilistic causal Bayesian networks.

Findings

Provides a sound and complete axiomatization for the nondeterministic causal logic.

Shows how to identify counterfactuals in probabilistic causal models.

Improves the realism of causal modeling by relaxing deterministic assumptions.

Abstract

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.