Sleeping Beauty Reconsidered: Conditioning and Reflection in Asynchronous Systems

Abstract

A careful analysis of conditioning in the Sleeping Beauty problem is done, using the formal model for reasoning about knowledge and probability developed by Halpern and Tuttle. While the Sleeping Beauty problem has been viewed as revealing problems with conditioning in the presence of imperfect recall, the analysis done here reveals that the problems are not so much due to imperfect recall as to asynchrony. The implications of this analysis for van Fraassen's Reflection Principle and Savage's Sure-Thing Principle are considered.Comment: A preliminary version of this paper appears in Principles of Knowledge Representation and Reasoning: Proceedings of the Ninth International Conference (KR 2004). This version will appear in Oxford Studies in Epistemolog