Graded epistemic logic with public announcement

Abstract

This work introduces a new fuzzy epistemic logic with public announcement with fuzzyness on both transitions and propositions. The interpretation of the connectives is done over the Gödel algebra and the interpretation of public announcements in this logic generalises the traditional update one. The core idea is that, the effect of a public announcement is reflected on the transitions degrees of the models. The update takes in account not only the truth degree of the announcement, at a target state, but also the degree of the transitions reaching that state. We prove the soundness of all axioms of the multi-agent epistemic logic with public announcements with respect to this graded semantics. Finally, we introduce the notion of bisimulation and prove the modal invariance property for our logic.