Description: Advanced ukasiewicz calculus and MV-algebras by D. Mundici This is a continuation of Vol. 7 of Trends in Logic. It wil cover the wealth of recent developments of Lukasiewicz Logic and their algebras (Chang MV-algebras), with particular reference to (de Finetti) coherent evaluation of continuously valued events, (Renyi) conditionals for such events, related algorithms. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description This is a continuation of Vol. 7 of Trends in Logic. It wil cover the wealth of recent developments of Lukasiewicz Logic and their algebras (Chang MV-algebras), with particular reference to (de Finetti) coherent evaluation of continuously valued events, (Renyi) conditionals for such events, related algorithms. Notes Written for self-studyReferences 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 eventsFocuses on Lukasiewicz logic and their algebras, because of the powerful mathematical tools available here Back Cover In recent years, the discovery of the relationships between formulas in lukasiewicz logic and rational polyhedra, Chang MV-algebras and lattice-ordered abelian roups, MV-algebraic states and coherent de Finettis 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 lukasiewicz logic and MV-algebras. Each chapter features a combination of classical and re Author Biography 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 Godel 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. Table of Contents Preface.- Chapter 1. Prologue: de Finetti coherence criterion and ukasiewicz logic.- Chapter 2. Rational polyhedra, Interpolation, Amalgamation.- Chapter 3. The Galois connection (Mod, Th) in ∞ 21.- Chapter 4. The spectral and the maximal spectral space.- Chapter 5. De Concini-Procesi theorem and Schauder bases.- Chapter 6. Bases and nitely presented MV-algebras.- Chapter 7. The free product of MV-algebras.- The construction of free products.- Chapter 8. Direct limits, conuence and multisets.- Chapter 9. Tensors.- Chapter 10. States and the Kroupa-Panti Theorem.- Chapter 11. The MV-algebraic Loomis-Sikorski theorem.- Chapter 12. The MV-algebraic Stone-von Neumann theorem.- Chapter 13. Recurrence, probability, measure.- Chapter 14. Measuring polyhedra and averaging truth-values.- Chapter 15. A Rényi conditional in ukasiewicz logic.- Chapter 16. The Lebesgue state and the completion of FREEn.- Chapter 17. Finitely generated projective MV-algebras.- Chapter 18. Eective procedures for ∞ and MV-algebras.- Chapter 19. A rst-order ukasiewicz logic with [0, 1]-identity.- Chapter 20. Applications, further reading, selected problems.- Chapter 21. Background results.- Special Bibliography. References. Index. Review 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 ukasiewicz 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 ukasiewicz logic … . Each chapter focuses on a specific topic and chapters are almost independent from each other." (Brunella Gerla, Zentralblatt MATH, Vol. 1235, 2012) Review Quote 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 ukasiewicz 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 ukasiewicz logic … . Each chapter focuses on a specific topic and chapters are almost independent from each other. (Brunella Gerla, Zentralblatt MATH, Vol. 1235, 2012) Feature 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 Details ISBN9400708394 Publisher Springer Series Trends in Logic Year 2011 ISBN-10 9400708394 ISBN-13 9789400708396 Format Hardcover Publication Date 2011-06-23 Imprint Springer Place of Publication Dordrecht Country of Publication Netherlands DEWEY 511.3 Edition 2011th Short Title ADVD LUKASIEWICZ CALCULUS & MV Language English Media Book Series Number 35 Pages 258 Illustrations XVIII, 258 p. DOI 10.1007/978-94-007-0840-2 Author D. 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ISBN-13: 9789400708396
Book Title: Advanced ukasiewicz calculus and MV-algebras
Number of Pages: 258 Pages
Language: English
Publication Name: Advanced Lukasiewicz Calculus and Mv-Algebras
Publisher: Springer
Publication Year: 2011
Subject: Mathematics
Item Height: 235 mm
Item Weight: 582 g
Type: Textbook
Author: D. Mundici
Item Width: 155 mm
Format: Hardcover
