On the sharpness and the injective property of basic justification models

TL;DR

This paper introduces a new decidable logic, Jref, that axiomatizes sharp and injective justification models, enhancing the modeling of epistemic scenarios like Russell's Prime Minister example.

Contribution

It provides the first axiomatization of sharp injective justification models within a decidable logic framework.

Findings

Jref is sound and complete for sharp injective models

Decidability of the logic Jref is established

Enhances epistemic modeling with justification logic

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.