Evidential decision theory via partial Markov categories

Partial Markov categories encode partial stochastic processes in the same way that Markov categories encode stochastic processes and restriction categories encode partial deterministic processes. The structure of partial Markov categories can express constraints, observations and updates. Thanks to these, we prove a synthetic Bayes theorem. We show how to model decision problems in partial Markov categories and solve them according to Evidential Decision Theory.
This is joint work with Mario Román.