Evaluations of epistemic components for resolving the muddy children puzzle

Kline, J. Jude (2013) Evaluations of epistemic components for resolving the muddy children puzzle. Economic Theory, 53 1: 61-83. doi:10.1007/s00199-012-0735-x

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Author Kline, J. Jude
Title Evaluations of epistemic components for resolving the muddy children puzzle
Journal name Economic Theory   Check publisher's open access policy
ISSN 0938-2259
Publication date 2013-05-01
Year available 2012
Sub-type Article (original research)
DOI 10.1007/s00199-012-0735-x
Open Access Status File (Author Post-print)
Volume 53
Issue 1
Start page 61
End page 83
Total pages 23
Place of publication Heidelberg, Germany
Publisher Springer
Collection year 2013
Language eng
Subject 1401 Economic Theory
Formatted abstract
We evaluate the 3 child muddy children puzzle using the epistemic logic of shallow depths GLEF. This system is used to evaluate what components are necessary for a resolution. These components include the basic beliefs of a child, the necessary depths of the epistemic structures, and the observations about the inactions of others added after a stage. These are all given explicitly, and their necessity is examined. We formulate the concept of a resolution as a process of inferences, actions, observations, and belief changes. We give three main theorems. The first one gives a very specific resolution, in which no common knowledge is involved. The second theorem states that any resolution has length of at least 3. The third theorem shows that the resolution given in the first theorem is minimal in various senses. In this manner, the necessary components for a resolution of the puzzle are evaluated. A final theorem gives a resolution for the n-child case.
Keyword Shallow depths of epistemic structures
Classical and epistemic inferences
Syntactic approach
Gentzen-style sequent calculus
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online: 9 December 2012

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2013 Collection
School of Economics Publications
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 2 times in Scopus Article | Citations
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Created: Mon, 19 Nov 2012, 18:17:32 EST by Jeffrey Kline on behalf of School of Economics