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.

Judea Pearl,
Probabilistic reasoning in intelligent systems,
Morgan Kaufmann, 1988
Here is a reference to a paper on extending belief propagation to
checking satisfiability of boolean formulas.