From Potential to Actual Knowledge: A New Framework in Probabilistic Epistemic Logic

Abstract In this paper we address the issue of improbable knowledge within probabilistic epistemic logic. This problem occurs when an agent possesses knowledge of a certain proposition despite the evidential probability of that knowledge being exceedingly low. The existence of such knowledge is paradoxical and poses significant challenges for probabilistic accounts of justification. We identify that the problem arises from assumptions about the non-transitivity of the epistemic accessibility relation which leads to the rejection of Axiom 4 according to which if one knows one knows that one knows. By redefining the epistemic operators we demonstrate that accepting Axiom 4 is feasible thus preventing improbable knowledge. Furthermore we explore the distinction between potential and actual knowledge as a solution to the problem of logical omniscience. We construct a probabilistic epistemic logic system that accurately models actual knowledge for agents with limited deductive abilities. Finally we introduce key semantic concepts for a dynamic probabilistic epistemic logic designed for non-omniscient agents providing a promising foundation for studying the dynamics of knowledge and its relationship with probability.