Tomás Orozco

• Tomás Orozco 29 Apr 2020 19:04 UTC

  1 point

  on: Defi­ni­tions of Causal Ab­strac­tion: Re­view­ing Beck­ers & Halpern

  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 $\tau$ - abstraction, there must be some surjective function ${\tau }_U$ that is compatible with $\tau$ . Hence, for constructive abstractions, must there also be mappings ${\tau }_U^1,\dots ,{\tau }_U^n$ such that, ${\tau }_U\left({\overrightarrow{u}}_L\right)={\tau }_U^1\left({\overrightarrow{z}}_U^1\right)\cdot \dots \cdot {\tau }_U^n\left({\overrightarrow{z}}_U^n\right)$ , where ${\overrightarrow{z}}_U^i$ is the projection of ${\overrightarrow{u}}_L$ onto the variables in ${\overrightarrow{Z}}_U^i$ ? 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 ${\tau }_U$ in the definition of constructive abstraction..

  Thank you!