An Epistemic Probabilistic Logic with Conditional Probabilities

Abstract

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 axiomatize this logic, provide corresponding semantics and prove that the axiomatization is sound and strongly complete. We also show that the logic is decidable.