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|a 9789400708402
|9 978-94-007-0840-2
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|a 10.1007/978-94-007-0840-2
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|a Mundici, D.
|e author.
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|a Advanced Łukasiewicz calculus and MV-algebras
|h [electronic resource] /
|c by D. Mundici.
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|a Dordrecht :
|b Springer Netherlands,
|c 2011.
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|a XVIII, 258 p.
|b online resource.
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|a text
|b txt
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|a Trends in Logic ;
|v 35
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|a 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.
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|a 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.
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|a Mathematics.
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|a Mathematical logic.
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|a Mathematics.
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|a Mathematical Logic and Foundations.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9789400708396
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|a Trends in Logic ;
|v 35
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|u http://dx.doi.org/10.1007/978-94-007-0840-2
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a Mathematics and Statistics (Springer-11649)
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