Fuzzy Logic of Quasi-Truth: An Algebraic Treatment [electronic resource] / by Antonio Di Nola, Revaz Grigolia, Esko Turunen.
By: Di Nola, Antonio [author.]
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Contributor(s): Grigolia, Revaz [author.] | Turunen, Esko [author.] | SpringerLink (Online service).
Material type: 
BookSeries: Studies in Fuzziness and Soft Computing: 338Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Edition: 1st ed. 2016.Description: VI, 116 p. 3 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319304069.Subject(s): Computational intelligence | Universal algebra | Computer science—Mathematics | Computational Intelligence | General Algebraic Systems | Symbolic and Algebraic ManipulationAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 006.3 Online resources: Click here to access online
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Springer Nature eBookSummary: 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.
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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