Abstract
In this paper, I propose a new version of probabilistic dynamic epistemic logic (GIPDEL) that is based on general imaging, and sketch the proof of soundness and completeness of this logic. The Monty Hall dilemma is a common topic in probabilistic dynamic epistemic logic. Using conditionalisation-based probabilistic dynamic epistemic logic (CPDEL), Kooi ([7]) supported the answer that I should switch my choice. However, it is acknowledged that this answer is counterintuitive. Using GIPDEL, I can support the answer that I do not have to switch my choice. Intuition would suggest this answer. Moreover, GIPDEL can give a plausible answer to a modified version of the Monty Hall dilemma to which CPDEL gives an extremely counterintuitive answer.
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References
Fagin, R., Halpern, J.Y.: Reasoning about Knowledge and Probability. Journal of the Association for Computing Machinery 41, 340–367 (1994)
Fagin, R., Halpern, J.Y.: Corrigendum: Reasoning about Knowledge and Probability. Journal of the Association for Computing Machinery 45, 214 (1998)
Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States. The MIT Press, Cambridge (1988)
Gerbrandy, J.: Bisimulation on Planet Kripke. ILLC Dissertation Series. ILLC, Amsterdam (1999)
Ichikawa, S.: Studies in Understanding Probability (in Japanese). Kyoritsu, Tokyo (1998)
Kooi, B.P.: Knowledge, Chance, and Change. ILLC Dissertation Series. ILLC, Amsterdam (2003)
Kooi, B.P.: Probabilistic Dynamic Epistemic Logic. Journal of Logic, Language and Information 12, 381–408 (2003)
Lewis, D.: Counterfactuals. Basil Blackwell, Oxford (1973)
Lewis, D.: Probabilities of Conditionals and Conditional Probabilities (rep in Lewis, D.: Philosophical Papers II, pp. 133–152. Oxford UP, Oxford (1986)). Philosophical Review 85, 297–315 (1976)
Suzuki, S.: On Imaging (in Japanese). Philosophical Studies (University of Tokyo) 17, 24–40 (1999)
Suzuki, S.: Imaging Reconsidered (in Japanese). Philosophical Studies (University of Tokyo) 18, 79–102 (2000)
Suzuki, S.: Belief Changes Represented by Imaging (in Japanese). The Autumn Regular Meeting, the Japan Association for Philosophy of Science (2004)
van Benthem, J.: Conditional Probability Meets Update Logic. Journal of Logic, Language and Information 12, 409–421 (2003)
Vos Savant, M.: The Power of Logical Thinking. St. Martin’s Press, New York (1996)
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Suzuki, S. (2007). Prolegomena to General-Imaging-Based Probabilistic Dynamic Epistemic Logic. In: Washio, T., Satoh, K., Takeda, H., Inokuchi, A. (eds) New Frontiers in Artificial Intelligence. JSAI 2006. Lecture Notes in Computer Science(), vol 4384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69902-6_12
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DOI: https://doi.org/10.1007/978-3-540-69902-6_12
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