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Negation of Graded Beliefs

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

Abstract

Negation is a key element in the construction of logical systems and plays a central role in reasoning and information manipulation tools. This paper considers the issue of negating graded beliefs, in the framework of a graded doxastic logic. It studies three interpretations of negation for these high level pieces of information, where negation is transferred to the three components of graded beliefs: the formula about which a belief is expressed, the belief modality and the belief level. The paper discusses the choice of appropriate formal frameworks for each of them, considering modal, fuzzy and many-valued logics; it characterises their use and underlines their relations, in particular regarding their effects on the belief degrees.

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Author information

Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606, 4 Place Jussieu, 75005, Paris, France

    Bénédicte Legastelois & Marie-Jeanne Lesot

  2. Université Paris 8 - EA 4383 - LIASD, 93526, Saint-Denis, France

    Adrien Revaultd’Allonnes

Authors
  1. Bénédicte Legastelois
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  2. Marie-Jeanne Lesot
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  3. Adrien Revaultd’Allonnes
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Corresponding author

Correspondence to Bénédicte Legastelois .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

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© 2016 Springer International Publishing Switzerland

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Legastelois, B., Lesot, MJ., Revaultd’Allonnes, A. (2016). Negation of Graded Beliefs. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_13

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  • DOI: https://doi.org/10.1007/978-3-319-40581-0_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40580-3

  • Online ISBN: 978-3-319-40581-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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