English

Evidential Decision Theory via Partial Markov Categories

Logic in Computer Science 2025-04-21 v4 Category Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2301.12989,
  title  = {Evidential Decision Theory via Partial Markov Categories},
  author = {Elena Di Lavore and Mario Román},
  journal= {arXiv preprint arXiv:2301.12989},
  year   = {2025}
}

Comments

22 pages. Presented at LiCS'23. This version repairs a problem with Proposition 5.2 without major changes; we thank Mark Szeles for pointing it out. This version substitutes 'probability of success' for 'probability of failure' in multiple places; we thank Paolo Perrone for noticing this typo

R2 v1 2026-06-28T08:26:57.823Z