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A Logic for Preference Lifting Under Uncertainty and Its Decidability

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Logic and Argumentation (CLAR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14156))

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Abstract

This paper explores the idea of the preference lifting under uncertainty. An attempt is proposed in the direction of “qualitative = qualitative + quantitative”. This leads to a novel lifting called the “pairwise lifting method”. It defines a \(\lambda \) function to record the number of occurrences of “\(\ge \) -binary relation” and “\(\le \) -binary relation” between individuals, and the preference relation between sets of individuals can be defined. We consider the logic of preference lifting of arbitrary preference relations, and prove its decidability by two methods, namely reduction to Presburger arithmetic and reduction to linear integer arithmetic.

The research of the first author is supported by Tsinghua University Initiative Scientific Research Program. The research of the second author is supported by the Taishan Young Scholars Program of the Government of Shandong Province, China (No. tsqn201909151).

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Notes

  1. 1.

    The same question can be asked about lifting preference over objects to that of sets of objects. We will not make distinction between worlds and objects in this paper.

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Author information

Authors and Affiliations

  1. China University of Political Science and Law, Beijing, China

    Xiaoxuan Fu

  2. Taishan University, Tai’an, China

    Zhiguang Zhao

Authors
  1. Xiaoxuan Fu
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  2. Zhiguang Zhao
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Corresponding author

Correspondence to Zhiguang Zhao .

Editor information

Editors and Affiliations

  1. IRIT CNRS, Toulouse, France

    Andreas Herzig

  2. Zhejiang University, Hangzhou, China

    Jieting Luo

  3. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Pere Pardo

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Fu, X., Zhao, Z. (2023). A Logic for Preference Lifting Under Uncertainty and Its Decidability. In: Herzig, A., Luo, J., Pardo, P. (eds) Logic and Argumentation. CLAR 2023. Lecture Notes in Computer Science(), vol 14156. Springer, Cham. https://doi.org/10.1007/978-3-031-40875-5_13

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  • DOI: https://doi.org/10.1007/978-3-031-40875-5_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40874-8

  • Online ISBN: 978-3-031-40875-5

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