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International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2014: Information Processing and Management of Uncertainty in Knowledge-Based Systems pp 385–394Cite as

Exploring Infinitesimal Events through MV-algebras and non-Archimedean States

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Part of the Communications in Computer and Information Science book series (CCIS,volume 443)

Abstract

In this paper we use tools from the theory of MV-algebras and MV-algebraic states to study infinitesimal perturbations of classical (i.e. Boolean) events and their non-Archimedean probability. In particular we deal with a class of MV-algebras which can be roughly defined by attaching a cloud of infinitesimals to every element of a finite Boolean algebra and for them we introduce the class of Chang-states. These are non-Archimedean mappings which we prove to be representable in terms of a usual (i.e. Archimedean) probability measure and a positive group homomorphism capable to handle the infinitesimal side of the MV-algebras we are dealing with. We also study in which relation Chang-states are with MV-homomorphisms taking value in a suitable perfect MV-algebra.

Keywords

  • MV-algebras
  • non-Archimedean states
  • probability measures

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  • DOI: 10.1007/978-3-319-08855-6_39
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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Romania

    Denisa Diaconescu

  2. DiSTA - Department of Theoretical and Applied Science, University of Insubria, Italy

    Anna Rita Ferraioli, Tommaso Flaminio & Brunella Gerla

Authors
  1. Denisa Diaconescu
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  2. Anna Rita Ferraioli
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  3. Tommaso Flaminio
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  4. Brunella Gerla
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Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. LIRMM, UMR CNRS/Universite Montpellier II, 161 rue Ada, 34392, Montpellier cedex 5, France

    Olivier Strauss

  3. UPMC Univ. Paris 06, CNRS UMR 7606, LIP6, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2014 Springer International Publishing Switzerland

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Diaconescu, D., Ferraioli, A.R., Flaminio, T., Gerla, B. (2014). Exploring Infinitesimal Events through MV-algebras and non-Archimedean States. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-08855-6_39

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  • DOI: https://doi.org/10.1007/978-3-319-08855-6_39

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08854-9

  • Online ISBN: 978-3-319-08855-6

  • eBook Packages: Computer ScienceComputer Science (R0)