The goal of Part VII is to introduce probabilistic models and reasoning. Principles of counting make up the foundation of the probabilistic approach. Before we get into the details of Bayes’ theorem, ► Chap. 22 , dynamic Bayesian models, ► Chap. 23 , and further stochastic techniques, ► Chap. 24 , we review the fundamentals of counting algorithms and the set theoretic constraints that constitute the foundation for probabilistic reasoning.