Algebraic Foundations of Many-Valued Reasoning

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these matters in detail, and gives a coherent presentation of the core results of the last 15 years or so, also adding unpublished material of the authors.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

Author(s): Roberto L. O. Cignoli, Itala M. L. D’Ottaviano, Daniele Mundici
Series: Trends in Logic 7
Publisher: Springer
Year: 2000

Language: English
Pages: 233
Tags: Logic; Order, Lattices, Ordered Algebraic Structures; Mathematical Logic and Foundations; Discrete Mathematics in Computer Science; Artificial Intelligence (incl. Robotics)

Front Matter....Pages i-ix
Introduction....Pages 1-6
Basic notions....Pages 7-30
Chang completeness theorem....Pages 31-49
Free MV-algebras....Pages 51-76
Łukasiewicz ∞-valued calculus....Pages 77-102
Ulam’s game....Pages 103-107
Lattice-theoretical properties....Pages 111-138
MV-algebras and ℓ-groups....Pages 139-156
Varieties of MV-algebras....Pages 157-178
Advanced topics....Pages 179-195
Further Readings....Pages 197-202
Back Matter....Pages 203-233