The main motivation for partial Markov categories is that Markov categories do not derive updates.
Topics.
- Normalization can be syntactically characterized in partial Markov categories.
- Bayes update can be formulated in subdistributions, synthetically: in a general partial Markov category, this is the synthetic Bayes theorem.
- Every partial Markov induces an order on morphisms, the quasitotal preorder.
- Newcomb’s problem can be formulated in the syntax of partial Markov.
- Quasitotal conditionals are a flavour of conditionals with a deterministic domain.
- normalization is almost a restriction operator notes how normalization is a restriction operator, modulo the last of the axioms. More broadly, the diagrams for normalization are those of an extension in the setting of cartesian restriction categories.
- Every partial Markov has a preorder enrichment, the quasitotal preorder.
- The simple syntax of partial Markov categories could be explained to the early ChatGPT, having it write code that can be later verified.
Literature.