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Algebraic Foundations of Many-Valued Reasoning by Daniele Mundici, Itala M. d'Ottaviano, R.L. Cignoli (Hardcover, 1999)

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This textbook states and proves theorems of many-valued propositional logic and provides the reader with recent developments and trends, including applications to adaptive error-correcting binary search. The book should be suitable for self-study, making the basic tools of 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 many-valued 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 specialized topics.