# Algebraization of Bayesian networks?

The algebraization of classical propositional logic is Boolean algebra.

Bayesian networks are a generalization of classical propositional logic with probability truth-values.

What is the corresponding algebraic form of Bayesian networks? Or at least outline how such an algebra would look like? I seem to be at a loss as to how to begin...

A bayesian network corresponds to an independence (algebraic) variety and hence to a polynomial ring over $\mathbb{R}$. You can start from