Most of the literature on causality considers the structural framework of Pearl and the potential-outcome framework of Neyman and Rubin to be formally equivalent, and therefore interchangeably uses the do-notation and the potential-outcome subscript notation to write counterfactual outcomes. In this paper, we superimpose the two causal frameworks to prove that structural counterfactual outcomes and potential outcomes do not coincide in general -- not even in law. More precisely, we express the law of the potential outcomes in terms of the latent structural causal model under the fundamental assumptions of causal inference. This enables us to precisely identify when counterfactual inference is or is not equivalent between approaches, and to clarify the meaning of each kind of counterfactuals.

翻译：关于因果关系的文献大多认为Pearl的结构化框架与Neyman和Rubin的潜在结果框架在形式上是等价的，因此常互换使用do-符号和潜在结果下标符号来表示反事实结果。本文通过叠加这两种因果框架，证明结构反事实结果与潜在结果在通常情况下并不一致——即使在分布层面也不等同。更具体地说，我们在因果推断的基本假设下，用潜在结构因果模型表达了潜在结果的分布规律。这使我们能够精确识别反事实推断在不同方法之间何时等价或不等价，并阐明各类反事实的含义。