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.

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

Autorentext

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.

Klappentext
In recent years, the discovery of the relationships between formulas in ukasiewicz 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 innite-valued ukasiewicz 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 eective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in ukasiewicz logic. The book embodies the viewpoint that modern ukasiewicz 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 renable partitions of unity, and rst-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.

Inhalt
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.