Fuzzy Logic of Quasi-Truth: An Algebraic Treatment

Nonfiction, Science & Nature, Mathematics, Algebra, Computers, Advanced Computing, Artificial Intelligence, General Computing
Cover of the book Fuzzy Logic of Quasi-Truth: An Algebraic Treatment by Antonio Di Nola, Revaz Grigolia, Esko Turunen, Springer International Publishing
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Author: Antonio Di Nola, Revaz Grigolia, Esko Turunen ISBN: 9783319304069
Publisher: Springer International Publishing Publication: March 18, 2016
Imprint: Springer Language: English
Author: Antonio Di Nola, Revaz Grigolia, Esko Turunen
ISBN: 9783319304069
Publisher: Springer International Publishing
Publication: March 18, 2016
Imprint: Springer
Language: English

This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic.  It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate Łukasiewicz logic is not complete with respect to the canonical set of truth values.  However, it is complete with respect to all linearly ordered MV –algebras.  As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.

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This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic.  It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate Łukasiewicz logic is not complete with respect to the canonical set of truth values.  However, it is complete with respect to all linearly ordered MV –algebras.  As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.

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