Identifying causal effects from observational data normally requires a fully specified causal graph, an assumption that becomes unrealistic in high‑dimensional or complex domains. Causal abstractions alleviate this requirement by retaining only partial causal information, thereby defining equivalence classes of compatible graphs. In this work we examine identifiability directly at the level of these graph collections rather than at the level of individual diagrams. Several notions of identifiability are formalized within this setting and arranged into a strict hierarchy that clarifies their inter‑relationships and distinctions. A central finding is that a causal effect may be identifiable over an entire collection of graphs even though no single causal derivation holds uniformly across all compatible graphs. These insights expose gaps and resolve ambiguities in the current literature.
Review