A Logic for Reasoning about Justified Uncertain Beliefs

Justification logic originated from the study of the logic of proofs. However, in a more general setting, it may be regarded as a kind of explicit epistemic logic. In such logic, the reasons why a fact is believed are explicitly represented as justification terms. Traditionally, the modeling of uncertain beliefs is crucially important for epistemic reasoning. While graded modal logics interpreted with possibility theory semantics have been successfully applied to the representation and reasoning of uncertain beliefs, they cannot keep track of the reasons why an agent believes a fact. The objective of this paper is to extend the graded modal logics with explicit justifications. We introduce a possibilistic justification logic, present its syntax and semantics, and investigate its meta-properties, such as soundness, completeness, and realizability.