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Fuzzy Logic of Quasi-Truth: An Algebraic Treatment

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  • © 2016

Overview

Authors:
  1. Antonio Di Nola

    1. University of Salerno, Fisciano, Italy

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  2. Revaz Grigolia

    1. University, Ivane Javakhishvili Tbilisi State, Tbilisi, Georgia

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  3. Esko Turunen

    1. Tampere University of Technology, Tampere, Finland

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  • Presents the first algebraic treatment of quasi-truth fuzzy logic
  • Covers the algebraic foundations of many-valued logic
  • Written by experts in the field

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 338)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-vi
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  2. Introduction

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 1-5

  3. Basic Notions

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 7-18

  4. Classical Sentential Calculus and Łukasiewicz Sentential Calculus

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 19-25

  5. MV-Algebras: Generalities

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 27-32

  6. Local MV-Algebras

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 33-36

  7. Perfect MV-Algebras

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 37-46

  8. The Variety Generated by Perfect MV-Algebras

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 47-51

  9. Representations of Perfect MV-Algebras

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 53-70

  10. The Logic of Perfect Algebras

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 71-84

  11. The Logic of Quasi True

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 85-89

  12. Perfect Pavelka Logic

    • Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 91-109

  13. Back Matter

    Pages 111-116
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Keywords

About this book

This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic.  It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate Łukasiewicz logic is not complete with respect to the canonical set of truth values.  However, it is complete with respect to all linearly ordered MV –algebras.  As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.

Reviews

“This book studies many-valued logics and their algebraic counterparts which are suitable for formalizing and modelling the concept of quasi-true. … This work is a valuable source of information for all logicians and philosophers interested in mathematical models of vagueness, and their application to modelling many-valued truth-degrees in an algebraically coherent manner.” (Tomáš Kroupa, Mathematical Reviews, March, 2017)

Authors and Affiliations

  • University of Salerno, Fisciano, Italy

    Antonio Di Nola

  • University, Ivane Javakhishvili Tbilisi State, Tbilisi, Georgia

    Revaz Grigolia

  • Tampere University of Technology, Tampere, Finland

    Esko Turunen

Bibliographic Information

  • Book Title: Fuzzy Logic of Quasi-Truth: An Algebraic Treatment

  • Authors: Antonio Di Nola, Revaz Grigolia, Esko Turunen

  • Series Title: Studies in Fuzziness and Soft Computing

  • DOI: https://doi.org/10.1007/978-3-319-30406-9

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-30404-5Published: 30 March 2016

  • Softcover ISBN: 978-3-319-80801-7Published: 25 April 2018

  • eBook ISBN: 978-3-319-30406-9Published: 18 March 2016

  • Series ISSN: 1434-9922

  • Series E-ISSN: 1860-0808

  • Edition Number: 1

  • Number of Pages: VI, 116

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Computational Intelligence, General Algebraic Systems, Symbolic and Algebraic Manipulation

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