Generalized Kripke models for epistemic logic

Abstract

In this paper a generalization of Kripke models is proposed for systemizing the study of the many different epistemic notions that appear in the literature. The generalized Kripke models explicitly represent an agent's epistemic states to which the epistemic notions refer. Two central epistemic notions are identified: objective (S5) knowledge and rational introspective (KD45) belief. Their interaction is determined and a notion of justified true belief is explained in terms of them. The logic of this notion of justified true belief is shown to be S4.2, which is in accordance with a conjecture by Wolfgang Lenzen. The logic of justified belief is also determined.