Fuzzy Logic of Quasi-Truth: An Algebraic Treatment
Author:   Antonio Di Nola ,  Revaz Grigolia ,  Esko Turunen
Publisher:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2016
Volume:   338
ISBN:  

9783319808017


Pages:   116
Publication Date:   25 April 2018
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Fuzzy Logic of Quasi-Truth: An Algebraic Treatment


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Overview

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.

Full Product Details

Author:   Antonio Di Nola ,  Revaz Grigolia ,  Esko Turunen
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2016
Volume:   338
Dimensions:   Width: 15.50cm , Height: 0.70cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783319808017


ISBN 10:   331980801
Pages:   116
Publication Date:   25 April 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Introduction.- Basic Notions.- Classical Sentential Calculus and Lukasiewicz SententialCalculus.- 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.

Reviews

This book studies many-valued logics and their algebraic counterparts which are suitable for formalizing and modelling the concept of quasi-true. ... This work is a valuable source of information for all logicians and philosophers interested in mathematical models of vagueness, and their application to modelling many-valued truth-degrees in an algebraically coherent manner. (Tom�s Kroupa, Mathematical Reviews, March, 2017)


This book studies many-valued logics and their algebraic counterparts which are suitable for formalizing and modelling the concept of quasi-true. ... This work is a valuable source of information for all logicians and philosophers interested in mathematical models of vagueness, and their application to modelling many-valued truth-degrees in an algebraically coherent manner. (Tomas Kroupa, Mathematical Reviews, March, 2017)


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