On sharp and single-conclusion justification models

Justification awareness models (JAMs) were proposed by S. Artemov as a tool for modelling epistemic scenarios such as Russell’s prime minister example. It was demonstrated that the sharpness and the single-conclusion property of a model play an 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 $\textsf{J}_{\textit{ref}}$ that is sound and complete with respect to the class of all sharp single-conclusion justification models. We also provide the complete axiomatizations for the classes of all single-conclusion justification models and all sharp justification models.