No Finite Model Property for Logics of Quantified Announcements

TL;DR

This paper proves that certain logics involving quantification over public announcements do not have the finite model property, impacting understanding of their computational and logical characteristics.

Contribution

It establishes the negative result that these logics lack the finite model property, resolving an open question in the field.

Findings

Quantified announcement logics lack the finite model property.

The result connects to other open questions in epistemic logic.

Implications for the complexity and expressiveness of these logics.

Abstract

Quantification over public announcements shifts the perspective from reasoning strictly about the results of a particular announcement to reasoning about the existence of an announcement that achieves some certain epistemic goal. Depending on the type of the quantification, we get different formalisms, the most known of which are arbitrary public announcement logic (APAL), group announcement logic (GAL), and coalition announcement logic (CAL). It has been an open question whether the logics have the finite model property, and in the paper we answer the question negatively. We also discuss how this result is connected to other open questions in the field.