The Ladder of Causation describes three qualitatively different types of activities an agent may be interested in engaging in, namely, seeing (observational), doing (interventional), and imagining (counterfactual) (Pearl and Mackenzie, 2018). The inferential challenge imposed by the causal hierarchy is that data is collected by an agent observing or intervening in a system (layers 1 and 2), while its goal may be to understand what would have happened had it taken a different course of action, contrary to what factually ended up happening (layer 3). While there exists a solid understanding of the conditions under which cross-layer inferences are allowed from observations to interventions, the results are somewhat scarcer when targeting counterfactual quantities. In this paper, we study the identification of nested counterfactuals from an arbitrary combination of observations and experiments. Specifically, building on a more explicit definition of nested counterfactuals, we prove the counterfactual unnesting theorem (CUT), which allows one to map arbitrary nested counterfactuals to unnested ones. For instance, applications in mediation and fairness analysis usually evoke notions of direct, indirect, and spurious effects, which naturally require nesting. Second, we introduce a sufficient and necessary graphical condition for counterfactual identification from an arbitrary combination of observational and experimental distributions. Lastly, we develop an efficient and complete algorithm for identifying nested counterfactuals; failure of the algorithm returning an expression for a query implies it is not identifiable.

翻译：致癌的梯度描述了一种不同性质的活动类型,即:代理人可能有兴趣从事三种性质不同的活动,即观察(观察)、做(干预)和想象(反事实)(Pearl和Mackenzie,2018年)。因果等级的推论挑战在于,数据是由在系统(第1和第2层)中观察或干预的代理人收集的,而其目标可能是了解如果它采取了与事实结果相反的不同行动方针(第3层),就会发生什么样的情况。虽然对于允许从观察到干预的跨层推断(反事实)的条件有扎实的了解,但当瞄准反事实数量时,结果则有些少一些。在本文件中,我们研究将观察和实验任意组合起来的固定反事实。具体地说,在更明确的反事实定义的基础上,我们证明了完全的表达方式(CUT),它使得人们能够将任意的反事实归结为不真实的反事实。例如,在调解和公正分析中的应用通常要求一种直接、直接和直接的逻辑组合。