CannibalSmith, JacobLyles,

The emphasis on Bayesian probability is because it is the simplest way to extend classical logic to propositions with varying degrees of plausibility. Just as all classical logic can be reduced to repeated applications of modus ponens, all manipulations of plausibility can be reduced to applications of Bayes' Theorem (assuming you want results that will line up with classical logic as the plausibilities approach TRUE and FALSE).