Reasoning about knowledge and conditional probability

We present a proof-theoretical and model-theoretical approach to reasoning about knowledge and conditional probability. We extend both the language of epistemic logic and the language of linear weight formulas, allowing statements like “Agent Ag knows that the probability of A given B is at least a half”. We present both a propositional and a first-order version of the logic. We provide sound and complete axiomatizations for both logics and we prove decidability in the propositional case