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

TL;DR

This paper explores different semantic interpretations of public announcement operators within G"odel modal logic, revealing their expressive differences and providing partial completeness results for each interpretation.

Contribution

It introduces three distinct semantics for public announcements in G"odel modal logic and analyzes their expressive power and completeness properties.

Findings

Three semantic interpretations are proposed and shown to be distinct in expressive strength.

Partial completeness results are established for the introduced logics.

The semantics are based on [0,1]-valued generalizations of modal Kripke models.

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.