The classical notion of causal effect identifiability is defined in terms of treatment and outcome variables. In this paper, we consider the identifiability of state-based causal effects: how an intervention on a particular state of treatment variables affects a particular state of outcome variables. We demonstrate that state-based causal effects may be identifiable even when variable-based causal effects may not. Moreover, we show that this separation occurs only when additional knowledge -- such as context-specific independencies -- is available. We further examine knowledge that constrains the states of variables, and show that such knowledge can improve both variable-based and state-based identifiability when combined with other knowledge such as context-specific independencies. We finally propose an approach for identifying causal effects under these additional constraints, and conduct empirical studies to further illustrate the separations between the two levels of identifiability.

翻译：经典的因果效应可识别性概念是基于处理变量与结果变量定义的。本文探讨基于状态的因果效应可识别性：即对处理变量特定状态的干预如何影响结果变量的特定状态。我们证明，即使变量层面的因果效应不可识别，状态层面的因果效应仍可能可识别。此外，我们发现这种分离现象仅当存在额外知识（例如上下文特定独立性）时才会出现。我们进一步研究了约束变量状态的知识，并证明此类知识在与上下文特定独立性等其他知识结合时，能够同时提升变量层面与状态层面的可识别性。最后，我们提出了一种在这些额外约束下识别因果效应的方法，并通过实证研究进一步阐明了两个可识别性层次之间的分离关系。