Modelling uncertainty using probability, and belief propagation
Here are references to a couple of textbooks which describe
the belief propagation algorithms in detail and provide
the required background for modelling systems with
uncertainty using probability.
Here is a very readable book from one of the founders of the subject,
and winner of the Turing award for 2011.
Here is a reference to a paper on extending belief propagation to
checking satisfiability of boolean formulas.
Probabilistic reasoning in intelligent systems,
Morgan Kaufmann, 1988