Algebraic Foundations of Many-Valued Reasoning
Cignoli, Roberto; D'Ottaviano, Itala M.L.; Mundici, Daniele
ISBN 10: 9048153360 ISBN 13: 9789048153367
Editore: Springer, 2010
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Series: Trends in Logic. Num Pages: 233 pages, 1 black & white illustrations, biography. BIC Classification: HPL; PBC; PBF; UYA; UYQ. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 13. Weight in Grams: 379. . 2010. 1st ed. Softcover of orig. ed. 2000. Paperback. . . . . Books ship from the US and Ireland. Codice articolo V9789048153367
Riassunto:
This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's Mv algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics.
Recensione:
`Meanwhile, a rich structure theory for MV-algebras has been developed, relating them e.g. to l-groups and to nonstandard reals. The present book develops these matters in detail, and gives a coherent presentation of the core results of the last 15 years or so, also adding unpublished material of the authors. For future work on MV-algebras, this monograph will be an indispensable source.'
Mathematical Reviews, 2001
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Titolo: Algebraic Foundations of Many-Valued ...
Casa editrice: Springer
Data di pubblicazione: 2010
Legatura: Brossura
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Algebraic Foundations of Many-Valued Reasoning
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Introduction. 1. Basic notions. 2. Chang completeness theorem. 3. Free MV-algebras. 4. Lukasiewicz INFINITY-valued calculus. 5. Ulam s game. 6. Lattice-theoretical properties. 7. MV-algebras and l-groups. 8. Varieties of MV-algebras. 9. Advanced topics. Codice articolo 5819193
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Taschenbuch. Condizione: Neu. Algebraic Foundations of Many-Valued Reasoning | R. L. Cignoli (u. a.) | Taschenbuch | ix | Englisch | 2010 | Springer | EAN 9789048153367 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Codice articolo 107246184
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Algebraic Foundations of Many-Valued Reasoning (Trends in Logic)
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Condizione: New. Codice articolo ABLIING23Apr0316110336826
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Springer Netherlands, Springer Netherlands Dez 2010, 2010
ISBN 10: 9048153360
ISBN 13: 9789048153367
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The aim of this book is to give self-contained proofs of all basic results concerning the infinite-valued proposition al calculus of Lukasiewicz and its algebras, Chang's MV -algebras. This book is for self-study: with the possible exception of Chapter 9 on advanced topics, the only prere quisite for the reader is some acquaintance with classical propositional logic, and elementary algebra and topology. In this book it is not our aim to give an account of Lukasiewicz's motivations for adding new truth values: readers interested in this topic will find appropriate references in Chapter 10. Also, we shall not explain why Lukasiewicz infinite-valued propositionallogic is a ba sic ingredient of any logical treatment of imprecise notions: Hajek's book in this series on Trends in Logic contains the most authorita tive explanations. However, in order to show that MV-algebras stand to infinite-valued logic as boolean algebras stand to two-valued logic, we shall devote Chapter 5 to Ulam's game of Twenty Questions with lies/errors, as a natural context where infinite-valued propositions, con nectives and inferences are used. While several other semantics for infinite-valued logic are known in the literature-notably Giles' game theoretic semantics based on subjective probabilities-still the transi tion from two-valued to many-valued propositonallogic can hardly be modelled by anything simpler than the transformation of the familiar game of Twenty Questions into Ulam game with lies/errors.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 244 pp. Englisch. Codice articolo 9789048153367
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Algebraic Foundations of Many-Valued Reasoning
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Springer Netherlands Dez 2010, 2010
ISBN 10: 9048153360
ISBN 13: 9789048153367
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The aim of this book is to give self-contained proofs of all basic results concerning the infinite-valued proposition al calculus of Lukasiewicz and its algebras, Chang's MV -algebras. This book is for self-study: with the possible exception of Chapter 9 on advanced topics, the only prere quisite for the reader is some acquaintance with classical propositional logic, and elementary algebra and topology. In this book it is not our aim to give an account of Lukasiewicz's motivations for adding new truth values: readers interested in this topic will find appropriate references in Chapter 10. Also, we shall not explain why Lukasiewicz infinite-valued propositionallogic is a ba sic ingredient of any logical treatment of imprecise notions: Hajek's book in this series on Trends in Logic contains the most authorita tive explanations. However, in order to show that MV-algebras stand to infinite-valued logic as boolean algebras stand to two-valued logic, we shall devote Chapter 5 to Ulam's game of Twenty Questions with lies/errors, as a natural context where infinite-valued propositions, con nectives and inferences are used. While several other semantics for infinite-valued logic are known in the literature-notably Giles' game theoretic semantics based on subjective probabilities-still the transi tion from two-valued to many-valued propositonallogic can hardly be modelled by anything simpler than the transformation of the familiar game of Twenty Questions into Ulam game with lies/errors. 244 pp. Englisch. Codice articolo 9789048153367
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Algebraic Foundations of Many-Valued Reasoning
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Springer Netherlands, Springer Netherlands, 2010
ISBN 10: 9048153360
ISBN 13: 9789048153367
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - The aim of this book is to give self-contained proofs of all basic results concerning the infinite-valued proposition al calculus of Lukasiewicz and its algebras, Chang's MV -algebras. This book is for self-study: with the possible exception of Chapter 9 on advanced topics, the only prere quisite for the reader is some acquaintance with classical propositional logic, and elementary algebra and topology. In this book it is not our aim to give an account of Lukasiewicz's motivations for adding new truth values: readers interested in this topic will find appropriate references in Chapter 10. Also, we shall not explain why Lukasiewicz infinite-valued propositionallogic is a ba sic ingredient of any logical treatment of imprecise notions: Hajek's book in this series on Trends in Logic contains the most authorita tive explanations. However, in order to show that MV-algebras stand to infinite-valued logic as boolean algebras stand to two-valued logic, we shall devote Chapter 5 to Ulam's game of Twenty Questions with lies/errors, as a natural context where infinite-valued propositions, con nectives and inferences are used. While several other semantics for infinite-valued logic are known in the literature-notably Giles' game theoretic semantics based on subjective probabilities-still the transi tion from two-valued to many-valued propositonallogic can hardly be modelled by anything simpler than the transformation of the familiar game of Twenty Questions into Ulam game with lies/errors. Codice articolo 9789048153367
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