Towards an Epistemic Logic for Uncertain Agents

摘要

In this paper, we propose a logic for reasoning about probabilistic belief, called PBL_r. Our language introduces formulas that express "agent I believes that the probability of φ is at least p". We first provide an inference system of PBL_r, and then introduce a probabilistic semantics for PBL_r. The soundness and finite model property of PBL_r are proved, which ensure the weak completeness and decidability of PBL_r.