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International Workshop on Fuzzy Logic and Applications

WILF 2013: Fuzzy Logic and Applications pp 77–85Cite as

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

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Part of the Lecture Notes in Computer Science book series (LNAI,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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Author information

Authors and Affiliations

  1. Università di Salerno, Via Ponte don Melillo, Fisciano, 84084, Salerno, Italy

    Antonio Di Nola

  2. Università dell’Insubria, Via Mazzini 5, 21100, Varese, Italy

    Brunella Gerla

  3. University of Bucharest, Academiei 14, sector 1, C.P. 010014, Bucharest, Romania

    Ioana Leustean

Authors
  1. Antonio Di Nola
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  2. Brunella Gerla
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  3. Ioana Leustean
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Editor information

Editors and Affiliations

  1. DIBRIS, University of Genoa, Via Dodecaneso 35, 16146, Genoa, Italy

    Francesco Masulli

  2. Dept. of Informatics, Systems, and Communication, University of Milano Bicocca, Viale Sarca 336, 20126, Milan, Italy

    Gabriella Pasi

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

    Ronald Yager

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Di Nola, A., Gerla, B., Leustean, I. (2013). Adding Real Coefficients to Łukasiewicz Logic: An Application to Neural Networks. In: Masulli, F., Pasi, G., Yager, R. (eds) Fuzzy Logic and Applications. WILF 2013. Lecture Notes in Computer Science(), vol 8256. Springer, Cham. https://doi.org/10.1007/978-3-319-03200-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-03200-9_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03199-6

  • Online ISBN: 978-3-319-03200-9

  • eBook Packages: Computer ScienceComputer Science (R0)