Fuzzy logic of quasi-truth : an algebraic treatment /

Fuzzy logic of quasi-truth : an algebraic treatment /

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Bibliographic Details
Author / Creator:	Di Nola, Antonio, author.
Imprint:	Cham : Springer, 2016.
Description:	1 online resource (vi, 116 pages) : illustrations
Language:	English
Series:	Studies in fuzziness and soft computing, 1434-9922 ; volume 338 Studies in fuzziness and soft computing ; v. 338.
Subject:	Fuzzy logic. Fuzzy logic.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11254001

Hidden Bibliographic Details
Other authors / contributors:	Grigolia, Revaz, author. Turunen, Esko, 1955- author.
ISBN:	9783319304069 3319304062 3319304046 9783319304045 9783319304045
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. English. Online resource; title from PDF title page (SpringerLink, viewed March 23, 2016).
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.
Other form:	Printed edition: 9783319304045
Standard no.:	10.1007/978-3-319-30406-9

Table of Contents:

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.