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Mundici, D.

Advanced Lukasiewicz calculus and MV-algebras (Gebundene Ausgabe)

Reihe: Trends in Logic 35

Springer-Verlag GmbH, Springer Netherland, Juli 2011

Edition - 256 S. - Sprache: Englisch - 248x166x23 mm Book

ISBN: 9400708394 EAN: 9789400708396

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.

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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


Preface.- Chapter 1. Prologue: de Finetti coherence criterion and Lukasiewicz logic.- Chapter 2. Rational polyhedra, Interpolation, Amalgamation.- Chapter 3. The Galois connection (Mod, Th) in L8 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, con¿uence 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 Lukasiewicz logic.- Chapter 16. The Lebesgue state and the completion of FREEn.- Chapter 17. Finitely generated projective MV-algebras.- Chapter 18. E¿ective procedures for L8 and MV-algebras.- Chapter 19. A ¿rst-order Lukasiewicz logic with [0, 1]-identity.- Chapter 20. Applications, further reading, selected problems.- Chapter 21. Background results.- Special Bibliography. References. Index.

Über den Autor

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 G?del 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.


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 Lukasiewicz 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 Lukasiewicz logic ... . Each chapter focuses on a specific topic and chapters are almost independent from each other." (Brunella Gerla, Zentralblatt MATH, Vol. 1235, 2012)

ISBN 9-400708-39-4, ISBN 9-40-070839-4, ISBN 9-40070-839-4, ISBN 9-400-70839-4, ISBN 9-4007-0839-4

ISBN 978-9-400708-39-6, ISBN 978-9-40-070839-6, ISBN 978-9-40070-839-6, ISBN 978-9-400-70839-6, ISBN 978-9-4007-0839-6

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