Causal abstraction provides a theory describing how several causal models can represent the same system at different levels of detail. Existing theoretical proposals limit the analysis of abstract models to "hard" interventions fixing causal variables to be constant values. In this work, we extend causal abstraction to "soft" interventions, which assign possibly non-constant functions to variables without adding new causal connections. Specifically, (i) we generalize $\tau$-abstraction from Beckers and Halpern (2019) to soft interventions, (ii) we propose a further definition of soft abstraction to ensure a unique map $\omega$ between soft interventions, and (iii) we prove that our constructive definition of soft abstraction guarantees the intervention map $\omega$ has a specific and necessary explicit form.
翻译:因果抽象学提供了一种理论,描述了若干因果模型如何在不同的详细程度上代表同一系统。现有的理论提案将抽象模型的分析限于“硬”干预,将因果变量确定为不变值。在这项工作中,我们将因果抽象学扩大到“软”干预,这种“软”干预可能赋予变量非连续性功能,而不增加新的因果联系。具体地说,(一) 我们将Beckers和Halpern(2019年)的$tau$-abstraction概括为软干预,(二) 我们提出了软抽象化的进一步定义,以确保软干预之间有一个独特的$\omega$地图,以及(三) 我们证明我们对软抽象化的建设性定义保证了干预地图$\omega$有具体和必要的明确形式。