Algebraic Foundations of Many-Valued Reasoning

R. L. Cignoli (u. a.)

ISBN 10: 9048153360 / ISBN 13: 9789048153367

Published by Springer, 2010

About this Item

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.

Seller Inventory # 107246184

Bibliographic Details

• Title: Algebraic Foundations of Many-Valued Reasoning
• Publisher: Springer
• Publication Date: 2010
• Language: English
• ISBN 10: 9048153360
• ISBN 13: 9789048153367
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 14D millimeters 235 millimeters width by 155 millimeters height by 14 millimeters depth
• Weight: 376 grams
• Seller catalogs:
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About this title

Synopsis

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.

Review

`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these matters in detail, and gives a coherent presentation of the core results of the last 15 years or so, also adding unpublished material of the authors.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