Advanced Łukasiewicz calculus and MV-algebras

• Κύριος συγγραφέας: Mundici, D. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Dordrecht : Springer Netherlands, 2011.
• Σειρά: Trends in Logic ; 35
• Θέματα: 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 logic. This book is intended as an up-to-date monograph on infinite-valued Łukasiewicz 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 effective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in Łukasiewicz logic. The book embodies the viewpoint that modern Łukasiewicz 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 refinable partitions of unity, and first-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. 

 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.