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© 2016

Fuzzy Logic of Quasi-Truth: An Algebraic Treatment

Benefits

  • Presents the first algebraic treatment of quasi-truth fuzzy logic

  • Covers the algebraic foundations of many-valued logic

  • Written by experts in the field

Book

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

Table of contents

  1. Front Matter
    Pages i-vi
  2. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 1-5
  3. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 7-18
  4. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 19-25
  5. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 27-32
  6. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 33-36
  7. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 37-46
  8. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 47-51
  9. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 53-70
  10. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 71-84
  11. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 85-89
  12. Antonio Di Nola, Revaz Grigolia, Esko Turunen
    Pages 91-109
  13. Back Matter
    Pages 111-116

About this book

Introduction

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.

Keywords

Łukasiewicz Sentential Calculus MV-Algebra Local MV-Algebra Perfect MV-Algebra Mathematical Fuzzy Logic Pavelka-Style Fuzzy Logic Duality Of Categories Logic Of Quasi True Quasi Falsehood

Authors and affiliations

  1. 1.University of SalernoFiscianoItaly
  2. 2.UniversityIvane Javakhishvili Tbilisi StateTbilisiGeorgia
  3. 3.Tampere University of TechnologyTampereFinland

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
  • Series Abbreviated Title Studies in Fuzziness
  • DOI https://doi.org/10.1007/978-3-319-30406-9
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-30404-5
  • Softcover ISBN 978-3-319-80801-7
  • eBook ISBN 978-3-319-30406-9
  • Series ISSN 1434-9922
  • Series E-ISSN 1860-0808
  • Edition Number 1
  • Number of Pages VI, 116
  • Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
  • Topics Computational Intelligence
    General Algebraic Systems
    Symbolic and Algebraic Manipulation
  • Buy this book on publisher's site
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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)