Trends in Logic

Advanced Łukasiewicz calculus and MV-algebras

Authors: Mundici, D.

  • Written for self-study
  • References the self-contained book Trends in Logic 7 (co-authored by the same author)
  • Deals with the logic and probability of continuously-valued events, just as boolean logic deals with yes-no events
  • Focuses on Lukasiewicz logic and their algebras, because of the powerful mathematical tools available here
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About this book

In recent years, the discovery of the relationships between formulas in Łukasiewicz logic and rational polyhedra, Chang MV-algebras and lattice-ordered abelian roups, MV-algebraic states and coherent de Finetti’s assessments of continuous events, has changed the study and practice of many-valued logic. This book is intended as an up-to-date monograph on infinite-valued Łukasiewicz logic and MV-algebras. Each chapter features a combination of classical and re¬cent results, well beyond the traditional domain of algebraic logic: among others, a comprehensive account is given of many effective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in Łukasiewicz logic. The book embodies the viewpoint that modern Łukasiewicz logic and MV-algebras provide a benchmark for the study of several deep mathematical prob¬lems, such as Rényi conditionals of continuously valued events, the many-valued generalization of Carathéodory algebraic probability theory, morphisms and invari¬ant measures of rational polyhedra, bases and Schauder bases as jointly refinable partitions of unity, and first-order logic with [0,1]-valued identity on Hilbert space. Complete versions are given of a compact body of recent results and techniques, proving virtually everything that is used throughout, so that the book can be used both for individual study and as a source of reference for the more advanced reader.

About the authors

Daniele Mundici received his Laurea degree in Physics from the University of Modena. He is currently Professor of Mathematical Logic at the University of Florence, and has been Professor of Algorithms and Computability at the University of Milan.  

He has taught at universities in Europe, Africa and America.

He serves as a managing editor of various journals in logic, algebra and applied mathematics. He has been the President of the Kurt Gödel Society in Vienna and of the Italian Association for Logic and Applications. He is a member of the International Academy of Philosophy of Science, Bruxelles and a corresponding member of the National Academy of Exact Sciences, Buenos Aires.

He is the author of three books and over 140 research papers in logic, algebra and theoretical computer science.

Reviews

From the reviews:

“The book is recommended for professional researchers and advanced students with an appropriate mathematical background. The book covers most of the recent developments in Łukasiewicz infinite-valued calculus and MV-theory. … The presentation is clearly structured and self-contained. The book consists of twenty chapters and two appendices, and a suitable bibliography is offered at the end of each chapter. Some of the chapters can be read independently from the others.” (Manuela Busaniche, Mathematical Reviews, Issue 2012 i)

“The author of this book is one of the leading scientists in the field of MV-algebras, and in this work he presents his recent results, collecting them in a monograph that every scholar interested in many-valued logic should consult for his studies. The book is intended as a text for a second course on infinite-valued Łukasiewicz logic … . Each chapter focuses on a specific topic and chapters are almost independent from each other.” (Brunella Gerla, Zentralblatt MATH, Vol. 1235, 2012)


Table of contents (21 chapters)

  • Prologue: de Finetti Coherence Criterion and Łukasiewicz Logic

    Mundici, D.

    Pages 1-10

  • Rational Polyhedra, Interpolation, Amalgamation

    Mundici, D.

    Pages 11-25

  • The Galois Connection (Mod, Th) in Ł $$\infty$$

    Mundici, D.

    Pages 27-39

  • The Spectral and the Maximal Spectral Space

    Mundici, D.

    Pages 41-53

  • De Concini–Procesi Theorem and Schauder Bases

    Mundici, D.

    Pages 55-68

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-94-007-0840-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-94-007-0839-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-94-007-3660-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Advanced Łukasiewicz calculus and MV-algebras
Authors
Series Title
Trends in Logic
Series Volume
35
Copyright
2011
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-007-0840-2
DOI
10.1007/978-94-007-0840-2
Hardcover ISBN
978-94-007-0839-6
Softcover ISBN
978-94-007-3660-3
Series ISSN
1572-6126
Edition Number
1
Number of Pages
XVIII, 258
Topics