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Towards a Unified View on Logics for Uncertainty

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Scalable Uncertainty Management (SUM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13562))

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Abstract

In the present paper, we propose a general logical approach for reasoning about probability functions, belief functions, lower probabilities and the corresponding duals. The logical setting we consider combines the modal logic S5, Łukasiewicz logic and an additional modality P that applied to boolean formulas formalises probability functions. The modality P together with an S5 modal \(\Box \) provides a language rich enough to characterise probability, belief and lower probability theories.

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Acknowledgements

The authors thank the anonymous referees for their comments and suggestions. Corsi and Hosni acknowledge funding by the Department of Philosophy “Piero Martinetti” of the University of Milan under the Project “Departments of Excellence 2018–2022” awarded by the Ministry of Education, University and Research (MIUR). Flaminio acknowledges partial support by the Spanish project PID2019-111544GB-C21 and by the MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627). Hosni also acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, grant LA 4093/3-1).

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Authors and Affiliations

  1. Department of Philosophy, University of Milan, Via Festa del Perdono 7, 20122, Milano, Italy

    Esther Anna Corsi & Hykel Hosni

  2. Artificial Intelligence Research Institute (IIIA - CSIC), Campus UAB, Bellaterra, 08193, Spain

    Tommaso Flaminio

Authors
  1. Esther Anna Corsi
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  2. Tommaso Flaminio
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  3. Hykel Hosni
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Corresponding author

Correspondence to Esther Anna Corsi .

Editor information

Editors and Affiliations

  1. IRIT-Université Toulouse, Toulouse, France

    Florence Dupin de Saint-Cyr

  2. Université Paris-Dauphine - PSL, Paris, France

    Meltem Öztürk-Escoffier

  3. Imperial College London, London, UK

    Nico Potyka

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Corsi, E.A., Flaminio, T., Hosni, H. (2022). Towards a Unified View on Logics for Uncertainty. In: Dupin de Saint-Cyr, F., Öztürk-Escoffier, M., Potyka, N. (eds) Scalable Uncertainty Management. SUM 2022. Lecture Notes in Computer Science(), vol 13562. Springer, Cham. https://doi.org/10.1007/978-3-031-18843-5_22

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  • DOI: https://doi.org/10.1007/978-3-031-18843-5_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-18842-8

  • Online ISBN: 978-3-031-18843-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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