Algebraic Foundations of Many-Valued Reasoning / Edition 1

Algebraic Foundations of Many-Valued Reasoning / Edition 1

by R.L. Cignoli, Itala M. d'Ottaviano, Daniele Mundici
     
 

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ISBN-10: 0792360095

ISBN-13: 9780792360094

Pub. Date: 11/30/1999

Publisher: Springer Netherlands

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

Overview

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.

Product Details

ISBN-13:
9780792360094
Publisher:
Springer Netherlands
Publication date:
11/30/1999
Series:
Trends in Logic Series, #7
Edition description:
2000
Pages:
233
Product dimensions:
6.10(w) x 9.25(h) x 0.28(d)

Table of Contents

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. 10. Further Readings. Bibliography. Index.

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