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Advanced Łukasiewicz calculus and MV-algebras / by D. Mundici
(Trends in Logic, Studia Logica Library. ISSN:22127313 ; 35)
版 | 1st ed. 2011. |
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出版者 | (Dordrecht : Springer Netherlands : Imprint: Springer) |
出版年 | 2011 |
本文言語 | 英語 |
大きさ | XVIII, 258 p : online resource |
著者標目 | *Mundici, D author SpringerLink (Online service) |
件 名 | LCSH:Mathematical logic FREE:Mathematical Logic and Foundations |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-94-007-0840-2 |
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Springer eBooks | 9789400708402 |
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EB00234605 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA8.9-10.3 DC23:511.3 |
書誌ID | 4000118431 |
ISBN | 9789400708402 |
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