Abstracting Causal Models
  We consider a sequence of successively more restrictive definitions of
abstraction for causal models, starting with a notion introduced by Rubenstein
et al. (2017) called exact transformation that applies to probabilistic causal
models, moving to a notion of uniform transformation that applies to
deterministic causal models and does not allow differences to be hidden by the
"right" choice of distribution, and then to abstraction, where the
interventions of interest are determined by the map from low-level states to
high-level states, and strong abstraction, which takes more seriously all
potential interventions in a model, not just the allowed interventions. We show
that procedures for combining micro-variables into macro-variables are
instances of our notion of strong abstraction, as are all the examples
considered by Rubenstein et al.
