A note on a generalization of the Muddy Children puzzle

Authors:
Nina Gierasimczuk;Jakub Szymanik
Affiliations:
Groningen;Groningen
Venue:
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
Year:
2011

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Abstract

We study a generalization of the Muddy Children puzzle by allowing public announcements with arbitrary generalized quantifiers. We propose a new concise logical modeling of the puzzle based on the number triangle representation of quantifiers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specific informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a form of variety).