Update, Probability, Knowledge and Belief

The paper considers two kinds of models for logics of knowledge and be-lief, neighbourhood models and epistemic weight models, and traces con-nections. Epistemic weight models combine knowledge and probability by using epistemic accessibility relations and weights to define subjective prob-abilities. We present a new Probability Comparison Calculus that is sound and complete for epistemic weight models. This is a further simplification of the calculus for probabilistic epistemic weight models that was presented in AIML 2014. The paper gives a definition of generic epistemic probabilistic update, again a simplification of earlier proposals, with examples of how this is used in epistemic probabilistic model checking. This application illustrates, among other things, that update by public announcement and update by Bayesian conditioning are two sides of the same coin. We end with a pro-posal for capturing the distinction between risk and uncertainty in epistemi