A Probabilistic Semantics for Belief Logic

Abstract

Belief logic is one of the most important branches of philosophical logic. The standard approach for characterizing belief is based on the so-called possible worlds model within which the problem of logical omniscience is considered a significant defect. We present an alternative semantics for belief logic based on a probabilistic model, which formalizes the so-called Lockean thesis in philosophical literature. The Lockean thesis states that a person believes a proposition whenever they see that the probability of the proposition has reached or exceeded a prespecified threshold. We give a complete deductive system for probabilistic belief logic as well as detailed comparisons to existing frameworks of belief logic.