Algebraic Foundations of Many-Valued Reasoning: 7 - Brossura

Cignoli, R.L.; D'Ottaviano, Itala M.; Mundici, Daniele

Brossura

ISBN 10: 9048153360 ISBN 13: 9789048153367

Casa editrice: Springer, 2010

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.

Su questo libro

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these matters in detail, and gives a coherent presentation of the core results of the last 15 years or so, also adding unpublished material of the authors.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

Contenuti

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 9048153360
• ISBN 13: 9789048153367
• Rilegatura: Copertina flessibile
• Numero di pagine: 244
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania