TITLE: Algebraization of Bayesian networks?
QUESTION [6 upvotes]: 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...

REPLY [10 votes]: A bayesian network corresponds to an independence (algebraic) variety and hence to a polynomial ring over $\mathbb{R}$.
You can start from

Garcia, Luis David, Michael Stillman, and Bernd Sturmfels. "Algebraic
  geometry of Bayesian networks." Journal of Symbolic Computation 39.3-4
  (2005): 331-355.