Abstract
Hintikka and Sandu’s independence-friendly (IF) logic is a conservative extension of first-order logic that allows one to consider semantic games with imperfect information. In the present article, we first show how several variants of the Monty Hall problem can be modeled as semantic games for IF sentences. In the process, we extend IF logic to include semantic games with chance moves and dub this extension stochastic IF logic. Finally, we use stochastic IF logic to analyze the Sleeping Beauty problem, leading to the conclusion that the thirders are correct while identifying the main error in the halfers’ argument.
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Acknowledgements
The first author wishes to gratefully acknowledge the partial support of the European Science Foundation EUROCORES program LogICCC [FP002–Logic for Interaction (LINT)] and the Academy of Finland (Grant 129208).
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Presented by Yde Venema.
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Mann, A.L., Aarnio, V. A Logical Analysis of Monty Hall and Sleeping Beauty. Stud Logica 106, 1123–1162 (2018). https://doi.org/10.1007/s11225-017-9777-1
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DOI: https://doi.org/10.1007/s11225-017-9777-1