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Fuzzy logic of quasi-truth = an alge...

Di Nola, Antonio.

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Fuzzy logic of quasi-truth = an algebraic treatment /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Fuzzy logic of quasi-truth/ by Antonio Di Nola, Revaz Grigolia, Esko Turunen.
其他題名:	an algebraic treatment /
作者:	Di Nola, Antonio.
其他作者:	Grigolia, Revaz.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	vi, 116 p. :ill., digital ;24 cm.
內容註:	Introduction -- Basic Notions -- Classical Sentential Calculus and Lukasiewicz Sentential Calculus -- MV -Algebras: Generalities -- Local MV -algebras -- Perfect MV -algebras -- The Variety Generated by Perfect MV -algebras -- Representations of Perfect MV -algebras -- The Logic of Perfect Algebras -- The Logic of Quasi True -- Perfect Pavelka Logic.
Contained By:	Springer eBooks
標題:	Fuzzy logic. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-30406-9
ISBN:	9783319304069

Fuzzy logic of quasi-truth = an algebraic treatment /
Di Nola, Antonio.

Fuzzy logic of quasi-truthan algebraic treatment /[electronic resource] :by Antonio Di Nola, Revaz Grigolia, Esko Turunen. - Cham :Springer International Publishing :2016. - vi, 116 p. :ill., digital ;24 cm. - Studies in fuzziness and soft computing,v.3381434-9922 ;. - Studies in fuzziness and soft computing ;v.273..

Introduction -- Basic Notions -- Classical Sentential Calculus and Lukasiewicz Sentential Calculus -- MV -Algebras: Generalities -- Local MV -algebras -- Perfect MV -algebras -- The Variety Generated by Perfect MV -algebras -- Representations of Perfect MV -algebras -- The Logic of Perfect Algebras -- The Logic of Quasi True -- Perfect Pavelka Logic.

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 Lukasiewicz 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.

ISBN: 9783319304069

Standard No.: 10.1007/978-3-319-30406-9doiSubjects--Topical Terms:

532071
Fuzzy logic.

LC Class. No.: QA9.64

Dewey Class. No.: 511.313

Fuzzy logic of quasi-truth = an algebraic treatment /
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520 $a 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 Lukasiewicz 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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