Causal Modeling with Probabilistic Simulation Models
This work addresses foundational issues in causal modeling for AI and logic, but it is incremental as it builds on prior non-probabilistic simulation models.
The paper tackles the problem of extending conditional reasoning to probabilistic simulation models by defining probabilities on conditional formulas and proving foundational results, including a sound and complete axiomatization for linear inequalities with NP-completeness of satisfiability.
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this setting to the case of probabilistic simulation models. We give a natural definition of probability on formulas of the conditional language, allowing for the expression of counterfactuals, and prove foundational results about this definition. We also find an axiomatization for reasoning about linear inequalities involving probabilities in this setting. We prove soundness, completeness, and NP-completeness of the satisfiability problem for this logic.