The Relativity of Causal Knowledge: Backbone Identifiability under Private Knowledge

Complex causal models may contain far more detail than a shared task requires. A Markov kernel can retain the outcome distributions for selected interventions while omitting other variables and mechanisms. The Relativity of Causal Knowledge (RCK) framework organises communication of such distilled causal quantities along network paths, using shared, interventionally consistent abstractions at each step. This offers the potential to reduce communication demands and disclosure of models and data. We examine an identification requirement for realising that potential. For two causes of a common outcome, we establish local non-identifiability for general kernels under explicit conditions: complete separate intervention reports can leave the joint response undetermined. Known identification obstacles therefore persist in the abstract quantities, even when RCK transport is well defined. Under additive separability, identified response functions determine mean changes; the noise distribution additionally determines the full kernel. We thereby take a step towards operational RCK, highlighting the need to connect its communication framework with causal identification and distributed inference.