Di Nola / Grigolia / Turunen Fuzzy Logic of Quasi-Truth: An Algebraic Treatment

1. Auflage 2016
ISBN: 978-3-319-30406-9
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 338, 116 Seiten, eBook

Reihe: Studies in Fuzziness and Soft Computing

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.

Zielgruppe

Research

Autoren/Hrsg.

Di Nola, Antonio

Grigolia, Revaz

Turunen, Esko

Inhaltsverzeichnis

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.