A Note on a Generalization of the Muddy Children Puzzle

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 quantifi ers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specifi c informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quanti fier in the announcement is positively active (satis es a form of variety).
Keywords Muddy Children Puzzles  epistemic logic  generalized quantifiers
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Joshua Sack (2008). Temporal Languages for Epistemic Programs. Journal of Logic, Language and Information 17 (2):183-216.
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