A note on public announcements in standard G\"odel modal logic

Abstract

We study public announcement operators in the context of standard G\"odel modal logic as introduced by Caicedo and Rodriguez. Over that base logic, admitting a natural semantics over [0,1]-valued generalizations of modal Kripke models, we exhibit three possible semantic interpretations of the public announcement operator, all equivalent in a classical setting, and show that these logics are all different in terms of expressive strength. We provide partial completeness results for these logics via Hilbert-style calculi.