Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) 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 (A v B) > C at a causal model M as a weighted average of the probability of C in those submodels that truthmake A v B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). 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.

翻译：因果建模语义学（CMS，例如 Galles 和 Pearl 1998；Pearl 2000；Halpern 2000）是评估前件为原子公式合取的反事实的强大框架。我们将CMS扩展至对析取前件反事实概率的评估，并更一般地，扩展至前件为原子公式任意布尔组合的反事实。我们的核心思想是，在因果模型M中，为反事实 (A v B) > C 赋予概率，该概率等于在那些使A v B为真的子模型（Briggs 2012；Fine 2016, 2017）中C概率的加权平均值。子模型的权重由基于Eva、Stern和Hartmann（2019）提出的距离度量所确定的、到原始模型M的逆距离给出。除解决反事实认识论中的一个主要问题外，本文还展示了语义学、因果推断和形式认识论研究如何能够富有成效地结合。