Lukasiewicz-Moisil Algebras (Google eBook)

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Elsevier, May 13, 1991 - Mathematics - 582 pages
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The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.

This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.

Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.

  

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Contents

Chapter 1 Lattices Universal Algebra and Categories
1
Chapter 2 Topological Dualities in Lattice Theory
83
Chapter 3 Elementary Properties of LukasiewiczMoisil Algebras
105
Chapter 4 Connections With Other Classes of Lattices
165
Chapter 5 Filters Ideals and vCongruences
247
Chapter 6 Representation Theorems and Duality for LukasiewiczMoisilAlgebras
285
Chapter 7 Categorical Properties of LukasiewiczMoisil Algebras
359
Chapter 8 Monadic and Polyadic LukasiewiczMoisil Algebras
417
Chapter 9 Lukasiewicz Logics
459
Applications to Switching Theory
539
Rrferences
551
Author Index
575
Subject Index
579
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