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International Workshop on Logic, Rationality and Interaction

LORI 2021: Logic, Rationality, and Interaction pp 259–272Cite as

Representation Results for Non-cumulative Logics

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13039))

Abstract

Most (if not all) nonmonotonic logics are assumed to be cumulative, which is often regarded as the minimum requirement for a logic. We argue that cumulativity, in particular, cumulative transitivity can be abandoned, in order to better characterize reasoning in uncertainty. But giving up cumulative transitivity makes it hard to obtain representation results for these logics. Borrowing the idea from strict-tolerant logics, we give some representation results for nonmonotonic logics that are not cumulatively transitive.

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Acknowledgments

We thank two anonymous referees for their valuable comments. The first author of the paper was supported by National Social Science Foundation of China for key projects (No. 18ZDA033).

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Authors and Affiliations

  1. Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275, China

    Xuefeng Wen & Xincheng Luo

Authors
  1. Xuefeng Wen
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  2. Xincheng Luo
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Editors and Affiliations

  1. Indian Statistical Institute, Chennai, Tamil Nadu, India

    Sujata Ghosh

  2. Department of Philosophy, Stanford University, Stanford, CA, USA

    Thomas Icard

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Wen, X., Luo, X. (2021). Representation Results for Non-cumulative Logics. In: Ghosh, S., Icard, T. (eds) Logic, Rationality, and Interaction. LORI 2021. Lecture Notes in Computer Science(), vol 13039. Springer, Cham. https://doi.org/10.1007/978-3-030-88708-7_21

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