Muddy Waters

TL;DR

This paper introduces a novel hat problem with an unusual initial announcement, formalizing it using public announcement logic and its extension with fixpoints to analyze the information dynamics.

Contribution

It presents a new hat problem scenario and formalizes it within public announcement logic and fixpoint extensions, expanding the logical framework for such problems.

Findings

Formalization of the novel hat problem in public announcement logic

Extension of public announcement logic with fixpoints for this problem

Insights into information flow and knowledge updates in the scenario

Abstract

In the 2013 Advent calender of the Berlin Mathematics Research Center MATH+, Gerhard Woeginger presents a novel hat problem with an uncommon initial announcement. Although the information given is insufficient for the hat bearers to learn their colour, they are informed that the colours have been chosen so that they can learn their colour. We formalize this announcement in public announcement logic and in an extension of public announcement logic with fixpoints.