Evaluations of epistemic components for resolving the muddy children puzzle

J. Kline ()

Economic Theory, 2013, vol. 53, issue 1, 83 pages

Abstract: We evaluate the 3 child muddy children puzzle using the epistemic logic of shallow depths $$\text{ GL}_{EF}$$ . 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 theorems. The first one gives a 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. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Syntactic approach; Shallow depths of epistemic structures; Gentzen-style sequent calculus; Classical and epistemic inferences; D80; D83 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00199-012-0735-x

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