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Evidential Decision Theory via Partial Markov Categories
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We introduce partial Markov categories. In the same way that Markov categories encode stochastic processes, partial Markov categories encode stochastic processes with constraints, observations and updates. In particular, we prove a synthetic Bayes theorem and we apply it to define a syntactic partial theory of observations on any Markov category, whose normalisations can be computed in the original Markov category. Finally, we formalise Evidential Decision Theory in terms of partial Markov categories, and provide implemented examples.
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Cited by 2 Pith papers
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Finite Observations, Infinite Behaviour: bicategorical semantics for stateful monoidal processes
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Convex biproducts free-generate substochastic matrix categories isomorphic to probabilistic tape diagrams, giving a complete axiomatisation of probabilistic Boolean circuits.
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