Nondeterministic Causal Models

• URL: http://arxiv.org/abs/2405.14001v2
• Date: Sat, 24 Aug 2024 18:13:21 GMT
• Title: Nondeterministic Causal Models
• Authors: Sander Beckers,
• Abstract summary: We generalize acyclic deterministic structural equation models to the nondeterministic case. We provide a sound and complete axiomatization of the resulting logic.
• Score: 7.550566004119157
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We generalize acyclic deterministic structural equation models to the nondeterministic case and argue that it 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 we drop both of them in our proposal. We do so by allowing multi-valued functions in the structural equations. In addition, we adjust the semantics so that the solutions to the equations that obtained in the actual world are preserved in any counterfactual world. We 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 ours. Finally, we extend our models to the probabilistic case and show that they open up the way to identifying counterfactuals even in Causal Bayesian Networks.

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