Logic describes how repeated announcements change truth over time
Eventual and Strong Eventual Notions in Public Announcements
Logic in Computer ScienceMultiagent Systems
Summary
Some statements can change their truth value when announced publicly, sometimes becoming false after being true or vice versa. This paper explores new ways to understand what happens when announcements happen again and again, even infinitely many times. The authors study conditions where statements eventually settle into being true or false, and how fast this happens. They connect these ideas to well-known logical puzzles and show how different versions of these changes relate to each other.
What this means in practice
- •For security protocol designers: Better model and predict how knowledge changes during repeated public announcements in security or communication settings.
- •For interactive system developers: Design systems that reliably handle changing information states after multiple announcements or messages.
A theory result. No direct application yet.
Authors
Eiji Yamada
Abstract
In dynamic epistemic logic, the four notions of success, self-refutation, true lies, and impossible lies have been discussed in the context of public announcements. In this paper, we introduce eventual and strong eventual versions of these notions, as well as their transfinite versions, which allow transfinite iteration of announcements. We also introduce the notions of always informativeness when true or false. For example, a formula is eventually self-refuting if, whenever initially true, it eventually becomes false at some finite stage under iterated announcements, and strong eventual self-refutation further requires the formula to remain false at all sufficiently late stages. There are two main results. The first result gives the relationship among strong eventual notions, eventual notions, and several other conditions including conditions on the limit of the truth values of the announced formula, the uniform bound condition, and the fixed-point views of the Moore sentence and the self-fulfilling sentence. The second result gives the relationship among finite and transfinite versions of the eventual and strong eventual notions and the fixed-point views.