Adding Real Coefficients to Łukasiewicz Logic: An Application to Neural Networks

  • Antonio Di Nola
  • Brunella Gerla
  • Ioana Leustean
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8256)

Abstract

In this paper we shall deal with an extension of Łukasiewicz propositional logic obtained by considering scalar multiplication with real numbers, and we focus on the description of its Lindenbaum algebra, i.e., the algebra of truth functions. We show the correspondence between truth tables of such logic and multilayer perceptrons in which the activation function is the truncated identity.

Keywords

Many-valued logic Łukasiewicz logic McNaughton functions Neural Networks MV-algebras Riesz MV-algebras 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Antonio Di Nola
    • 1
  • Brunella Gerla
    • 2
  • Ioana Leustean
    • 3
  1. 1.Università di SalernoSalernoItaly
  2. 2.Università dell’InsubriaVareseItaly
  3. 3.University of BucharestBucharestRomania

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