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

  • Denisa Diaconescu
  • Anna Rita Ferraioli
  • Tommaso Flaminio
  • Brunella Gerla
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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Denisa Diaconescu
    • 1
  • Anna Rita Ferraioli
    • 2
  • Tommaso Flaminio
    • 2
  • Brunella Gerla
    • 2
  1. 1.Department of Computer Science, Faculty of Mathematics and Computer ScienceUniversity of BucharestRomania
  2. 2.DiSTA - Department of Theoretical and Applied ScienceUniversity of InsubriaItaly

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