# Advanced Łukasiewicz calculus and MV-algebras

Part of the Trends in Logic book series (TREN, volume 35)

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Part of the Trends in Logic book series (TREN, volume 35)

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.

MV-algebras conditioning fuzzy logic many-valued logic probability of continuously valued events

- DOI https://doi.org/10.1007/978-94-007-0840-2
- Copyright Information Springer Science+Business Media B.V. 2011
- Publisher Name Springer, Dordrecht
- eBook Packages Mathematics and Statistics
- Print ISBN 978-94-007-0839-6
- Online ISBN 978-94-007-0840-2
- Buy this book on publisher's site

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