Jeremy Goodman and Bernhard Salow recently proposed a probabilistic model for epistemology by using resources congenial to philosophers in the Bayesian tradition, which predicts only highly probable states are believed. It offers an adaptable definition of inductive knowledge and belief, and an intuitive expression of Bayesian inference. However, it is shown that a preference model can be generated from this which violates several syntax rules of cumulative logic (the corresponding logic to preference model).

Upon their work, we analyze the philosophical implication behind this failure, to clarify the principal difference between these semantics, which can be roughly explained by the distinction between the order of probability and the order of “preference”. And we explore a plausible way to transform their model to a labelled transition system, then use probabilistic modal logic semantic to match their idea.