Eventual and Strong Eventual Notions in Public Announcements
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.
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BibTeX
@misc{yamada2026eventual,
title = {{Eventual and Strong Eventual Notions in Public Announcements}},
author = {Eiji Yamada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24006},
eprint = {2609.24006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24006},
}
RIS
TY - UNPB
TI - Eventual and Strong Eventual Notions in Public Announcements
AU - Eiji Yamada
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24006
UR - https://arxiv.org/abs/2609.24006
AB - 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.
ER -