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Algebraic Foundations of Many-Valued Reasoning, Hardcover by Cignoli, Roberto...
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eBay-Artikelnr.:226691576734
Artikelmerkmale
- Artikelzustand
- Book Title
- Algebraic Foundations of Many-Valued Reasoning
- ISBN
- 9780792360094
Über dieses Produkt
Product Identifiers
Publisher
Springer Netherlands
ISBN-10
0792360095
ISBN-13
9780792360094
eBay Product ID (ePID)
1634440
Product Key Features
Number of Pages
IX, 233 Pages
Language
English
Publication Name
Algebraic Foundations of Many-Valued Reasoning
Subject
Algebra / Abstract, Logic
Publication Year
1999
Type
Textbook
Subject Area
Mathematics, Philosophy
Series
Trends in Logic Ser.
Format
Hardcover
Dimensions
Item Weight
54 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
99-052098
Dewey Edition
21
Reviews
' 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these matters in detail, and gives a coherent presentation of the core results of the last 15 years or so, also adding unpublished material of the authors.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, '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these matters in detail, and gives a coherent presentation of the core results of the last 15 years or so, also adding unpublished material of the authors.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
Series Volume Number
7
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
511.3
Table Of Content
1 Basic notions.- 2 Chang completeness theorem.- 3 Free MV-algebras.- 4 ?ukasiewicz ?-valued calculus.- 5 Ulam's game.- 6 Lattice-theoretical properties.- 7 MV-algebras and ?-groups.- 8 Varieties of MV-algebras.- 9 Advanced topics.- 10 Further Readings.
Synopsis
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., 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.
LC Classification Number
QA8.9-10.3
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