A note on public announcements in standard Gödel modal logic
Nicholas Pischke · arXiv (Cornell University) · 2017
We study public announcement operators in the context of standard Gödel 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.