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Structural causal models provide a formalism to express causal relationsbetween variables of interest. Models and variables can represent a system atdifferent levels of abstraction, whereby relations may be coarsened and refinedaccording to the need of a modeller. However, switching between differentlevels of abstraction requires evaluating a trade-off between the consistencyand the information loss among different models. In this paper we introduce afamily of interventional measures that an agent may use to evaluate such atrade-off. We consider four measures suited for different tasks, analyze theirproperties, and propose algorithms to evaluate and learn causal abstractions.Finally, we illustrate the flexibility of our setup by empirically showing howdifferent measures and algorithmic choices may lead to different abstractions.

Quantifying Consistency and Information Loss for Causal Abstraction Learning