Fuzzy Logic of Quasi-Truth: An Algebraic Treatment / by Antonio Di Nola, Revaz Grigolia, Esko Turunen
By: Di Nola, Antonio
Contributor(s): Grigolia, Revaz | Turunen, Esko
Material type: 
E-bookSeries: Studies in Fuzziness and Soft Computing; 338338Publisher: Cham : Springer International Publishing, 2016Edition: 1st ed.Description: 1 recurso en línea (VI, 116 p.) 3 il..ISBN: 9783319304069.Subject: Lógica difusaOnline resources: Acceso a este recurso digital (usuarios Universidad Europea de Madrid)
Summary: 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.
| Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | Item holds | |
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Madrid Digital Acceso Electrónico (UEM) | Ciencias e Ingeniería | QA9.64 D566 2016 EB (Browse shelf(Opens below)) | .i1159309x | Acceso electrónico | eBOOK .i1159309x |
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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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