Partial Markov Categories — Elena Di Lavore, Mario Román & Paweł Sobociński (2025). arXiv:2502.03477 (v4, PDF).
Introduces partial Markov categories — copy-discard categories with conditionals — as a setting for probabilistic reasoning with failure and exact observations; proves that the Kleisli category of the Maybe monad over a Markov category is one, develops a synthetic normalisation, compares Pearl’s and Jeffrey’s update rules, and proves a synthetic Bayes theorem.
Sources: the paper, arXiv:2502.03477v4, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 3.1: partial Markov category
- Definition 3.8, Propositions 3.11–3.12: normalisation
- Theorem 3.25: Kleisli categories of Maybe monads
- Definitions 4.7–4.8, Proposition 4.9: Pearl vs Jeffrey
- Definition 5.1, Theorem 5.4: exact observations and Bayes’ theorem
Concept notes
Partial Markov Category, Copy-Discard Category, Markov Category