统一图形与功能因果抽象，证明三类方法等价并拓展表达能力。
Aligning Graphical and Functional Causal Abstractions
- 提出图形与功能抽象的统一框架，建立一致性等价关系。
- 证明双射映射下簇图与α-抽象、τ-抽象在表达上等价。
- 引入部分簇图，增强图形抽象的灵活性和适用范围。
因果抽象使不同粒度层级的因果模型得以关联。为确保因果关系一致，现有框架定义了各类一致性概念。文献中两类主流方法为：(i) 图形抽象（如簇图），基于结构层面关联模型；(ii) 功能抽象（如α-抽象），通过变量及其取值范围间的映射关联模型。本文统一了图形与功能一致性概念，证明在抽象变量取值范围双射条件下，簇图、一致的α-抽象与构造性τ-抽象具有等价表达力。进一步，通过引入部分簇图，扩展了图形抽象的表达能力。研究结果建立了功能与图形框架之间的严格桥梁，支持二者间结论的迁移与应用。
原文摘要 · Abstract (English)
Causal abstractions allow us to relate causal models on different levels of granularity. To ensure that the models agree on cause and effect, frameworks for causal abstractions define notions of consistency. Two distinct methods for causal abstraction are common in the literature: (i) graphical abstractions, such as Cluster DAGs, which relate models on a structural level, and (ii) functional abstractions, like $α$-abstractions, which relate models by maps between variables and their ranges. In this paper we will align the notions of graphical and functional consistency and show an equivalence between the class of Cluster DAGs, consistent $α$-abstractions with the range of abstracted variables mapped bijectively, and constructive $τ$-abstractions. Furthermore, we extend this alignment and the expressivity of graphical abstractions by introducing Partial Cluster DAGs. Our results provide a rigorous bridge between the functional and graphical frameworks and allow for adoption and transfer of results between them.
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