Abstract
Based on a (total) pre-order on a set, we axiomatize the Egli-Milner order on the power set and show how it is related to the Lewis order. Moreover, we consider a strict version of the Egli-Milner order and show how it can be related to the semantics of conditionals based on a priority structure.
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Acknowledgements
Chenwei SHI is supported by the “Shuimu Scholars” postdoc program and the China Postdoctoral Science Foundation Grant (No. 2019M660705). Yang SUN is supported by the Major Program of the National Social Science Foundation of China (No. 17ZDA026). We would like to thank R. Ramanujam for bringing the issue of Egli-Milner ordering to our attention and Joe Halpern for his kind reply to our questions about his own work on order lifting. We also thank the two anonymous referees for their useful comments and suggestions. This work has been presented online at the ILLC LIRA Seminar in May 2020, and at the Logic Breakfast Session at the University of Bayreuth in July 2020. We want to thank the organizers, Fernando R. Velázquez-Quesada, Anthia Solaki and Olivier Roy, for inviting us, and the audience, especially Johan van Benthem, Rohit Parikh, Peter van Emde Boas, Alexandru Baltag, Zoé Christoff, Dominik Klein and Soroush Rafiee Rad, for their helpful feedback. At last, we would like to thank Fenrong Liu for her invaluable supervision and instructions.
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Shi, C., Sun, Y. Logic of Convex Order. Stud Logica 109, 1019–1047 (2021). https://doi.org/10.1007/s11225-020-09940-z
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DOI: https://doi.org/10.1007/s11225-020-09940-z