Advanced ¿ukasiewicz calculus and MV-algebras

2011
ISBN: 978-94-007-0839-6
Verlag: Springer Netherlands

Buch, Englisch, 258 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 582 g

Reihe: Trends in Logic

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.

Zielgruppe

Research

Autoren/Hrsg.

Mundici, D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

Preface.- Chapter 1. Prologue: de Finetti coherence criterion and Åukasiewicz logic.- Chapter 2. Rational polyhedra, Interpolation, Amalgamation.- Chapter 3. The Galois connection (Mod, Th) in Å∞ 21.- Chapter 4. The spectral and the maximal spectral space.- Chapter 5. De Concini-Procesi theorem and Schauder bases.- Chapter 6. Bases and ï¬nitely presented MV-algebras.- Chapter 7. The free product of MV-algebras.- The construction of free products.- Chapter 8. Direct limits, confluence 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 Åukasiewicz logic.- Chapter 16. The Lebesgue state and the completion of FREEn.- Chapter 17. Finitely generated projective MV-algebras.- Chapter 18. Effective procedures for Å∞ and MV-algebras.- Chapter 19. A ï¬rst-order Åukasiewicz logic with [0, 1]-identity.- Chapter 20. Applications, further reading, selected problems.- Chapter 21. Background results.- Special Bibliography. References. Index.

Über Autor(innen)

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.