Advanced Lukasiewicz calculus and MV-algebras [recurso electrónico] / by D. Mundici.

Por: Mundici, D [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: TextoTextoSeries Trends in Logic ; 35Editor: Dordrecht : Springer Netherlands, 2011Descripción: XVIII, 258 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9789400708402Tema(s): Mathematics | Logic, Symbolic and mathematical | Mathematics | Mathematical Logic and FoundationsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 511.3 Clasificación LoC:QA8.9-10.3Recursos en línea: Libro electrónicoTexto
Contenidos:
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.
En: Springer eBooksResumen: In recent years, the discovery of the relationships between formulas in Lukasiewicz 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 in?nite-valued Lukasiewicz 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 e?ective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in Lukasiewicz logic. The book embodies the viewpoint that modern Lukasiewicz 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 re?nable 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.
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Colección de Libros Electrónicos QA8.9 -10.3 (Browse shelf(Abre debajo)) 1 No para préstamo 378413-2001

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.

In recent years, the discovery of the relationships between formulas in Lukasiewicz 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 in?nite-valued Lukasiewicz 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 e?ective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in Lukasiewicz logic. The book embodies the viewpoint that modern Lukasiewicz 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 re?nable 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.

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