On the sharpness and the injective property of basic justification models

Abstract: Justification Awareness Models, JAMs, were proposed by S.~Artemov as a tool for modelling epistemic scenarios like Russel's Prime Minister example. It was demonstrated that the sharpness and the injective property of a model play essential role in the epistemic usage of JAMs. The problem to axiomatize these properties using the propositional justification language was left opened. We propose the solution and define a decidable justification logic Jref that is sound and complete with respect to the class of all sharp injective justification models.