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Probabilistic Three-Valued Argumentation Frameworks

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Logic and Argumentation (CLAR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12061))

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Abstract

Dung’ AF has been extended in many different directions. One particular direction is to allow uncertainty in AFs. Among others, probability and fuzzy theory are typical approaches used in this direction. In this paper, we argue that arguments can be both fuzzy and random. We thus introduce probabilistic-fuzzy argumentation frameworks in which probabilities and fuzzy values are combined to describe fuzzy and random arguments. We introduce an algorithm for revising probabilities. Based on this algorithm, we study semantics of probabilistic-fuzzy argumentation frameworks.

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Notes

  1. 1.

    If \(\mathbb {M}_A \le \mathbb {M}_B\) and \(\mathbb {M}_B \le \mathbb {M}_A\), \(\mathbb {M}_A = \mathbb {M}_B\). It is the same as the common “=” between matrices in algebra.

  2. 2.

    The two percentages 24% and 6% show the influence of the road working.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (11601288), the Natural Science Foundation of Shandong (ZR2016AQ21). The authors thank the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Jiachao Wu

  2. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, China

    Hengfei Li

Authors
  1. Jiachao Wu
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  2. Hengfei Li
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Correspondence to Hengfei Li .

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Editors and Affiliations

  1. Utrecht University, Utrecht, Utrecht, The Netherlands

    Mehdi Dastani

  2. Zhejiang University, Hangzhou, China

    Huimin Dong

  3. University of Luxembourg, Luxembourg, Luxembourg

    Leon van der Torre

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Wu, J., Li, H. (2020). Probabilistic Three-Valued Argumentation Frameworks. In: Dastani, M., Dong, H., van der Torre, L. (eds) Logic and Argumentation. CLAR 2020. Lecture Notes in Computer Science(), vol 12061. Springer, Cham. https://doi.org/10.1007/978-3-030-44638-3_19

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  • DOI: https://doi.org/10.1007/978-3-030-44638-3_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-44637-6

  • Online ISBN: 978-3-030-44638-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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