Skip to main content
SpringerLink
Log in

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

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belluce, P., Di Nola, A., Lettieri, A.: Local MV-algebras. Rend. Circ. Mat. Palermo 42, 347–361 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cignoli, R., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. Kluwer, Dordrecht (2000)

    Google Scholar 

  3. Diaconescu, D., Flaminio, T., Leuştean, I.: Lexicographic MV-algebras and lexicographic states (submitted)

    Google Scholar 

  4. Di Nola, A., Ferraioli, A.R., Gerla, B.: Combining Boolean algebras and ℓ-groups in the variety generated by Chang’s MV-algebra. Mathematica Slovaca (accepted)

    Google Scholar 

  5. Di Nola, A., Georgescu, G., Leustean, I.: States on Perfect MV-algebras. In: Novak, V., Perfilieva, I. (eds.) Discovering the World With Fuzzy Logic. STUDFUZZ, vol. 57, pp. 105–125. Physica, Heidelberg (2000)

    Google Scholar 

  6. Di Nola, A., Lettieri, A.: Perfect MV-algebras are categorically equivalent to abelian ℓ-groups. Studia Logica 53, 417–432 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  7. Mundici, D.: Averaging the truth-value in Łukasiewicz logic. Studia Logica 55(1), 113–127 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mundici, D.: Advanced Łukasiewicz calculus and MV-algebras. Trends in Logic, vol. 35. Springer (2011)

    Google Scholar 

  9. Paris, J.B.: The uncertain reasoner’s companion: A mathematical perspective. Cambridge University Press (1994)

    Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anna Rita Ferraioli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tommaso Flaminio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Brunella Gerla
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

  • 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)

Publish with us

Policies and ethics

Search

Navigation