Advanced Łukasiewicz calculus and MV-algebras

• Main Author: Mundici, D. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2011.
• Series: Trends in Logic ; 35
• Subjects: Mathematics.; Mathematical logic.; Mathematical Logic and Foundations.

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 log...

Table of Contents:

• Preface
• Chapter 1. Prologue: de Finetti coherence criterion and Łukasiewicz logic
• Chapter 2. Rational polyhedra, Interpolation, Amalgamation
• Chapter 3. The Galois connection (Mod, Th) in Ł∞ 21
• Chapter 4. The spectral and the maximal spectral space
• Chapter 5. De Concini-Procesi theorem and Schauder bases
• Chapter 6. Bases and finitely 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 Łukasiewicz logic
• Chapter 16. The Lebesgue state and the completion of FREEn
• Chapter 17. Finitely generated projective MV-algebras
• Chapter 18. Effective procedures for Ł∞ and MV-algebras
• Chapter 19. A first-order Łukasiewicz logic with [0, 1]-identity
• Chapter 20. Applications, further reading, selected problems
• Chapter 21. Background results
• Special Bibliography. References. Index.