Causal modeling semantics for counterfactuals with disjunctive antecedents

Causal Modeling Semantics (CMS, e.g., [6], [22], [12]) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual

at a causal model $M$ as a weighted average of the probability of C in those submodels that truthmake $A\vee B$ [1], [3], [4]. The weights of the submodels are given by the inverse distance to the original model $M$, based on a distance metric proposed by Eva et al. [2]. Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined.