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Comment by Tomás Orozco (tomas-orozco) on Definitions of Causal Abstraction: Reviewing Beckers & Halpern · 2020-04-29T19:04:06.560Z · LW · GW

Dear John Wentworth:

I have a doubt regarding the implications of Beckers' paper on abstractions. I am a lawyer by profession so I'm venturing pretty far afield here, and I hope my question will not be too trivial.

Given that every constructive abstraction is also a - abstraction, there must be some surjective function that is compatible with . Hence, for constructive abstractions, must there also be mappings such that, , where is the projection of onto the variables in ? In other words, must there also be a partition of the low-level exogenous variables where each partition is mapped to a distinct high-level variable? I missed in the definition of constructive abstraction..

Thank you!