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 Theta-valued algebras are presented, as well as Theta-algebras with negation. Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.
Author(s): V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu (Eds.)
Series: Annals of Discrete Mathematics 49
Publisher: Elsevier, Academic Press
Year: 1991
Language: English
Pages: ii-xv, 1-583
Content:
General Editor
Page ii
Edited by
Page iii
Copyright page
Page iv
Preface
Pages v-vii
List of Symbols
Pages xiii-xv
Chapter 1 Lattices, Universal Algebra and Categories
Pages 1-82
Chapter 2 Topological Dualities in Lattice Theory
Pages 83-104
Chapter 3 Elementary Properties of Lukasiewicz-Moisil Algebras
Pages 105-164
Chapter 4 Connections with Other Classes of Lattices
Pages 165-245
Chapter 5 Filters, Ideals and ϑ-Congruences
Pages 247-284
Chapter 6 Representation Theorems and Duality for Lmalgebras
Pages 285-358
Chapter 7 Categorical Properties of Lukasiewicz-Moisil Algebras
Pages 359-416
Chapter 8 Monadic and Polyadic Lukasiewicz-Moisil Algebras
Pages 417-458
Chapter 9 Lukasiewicz Logics
Pages 459-538
Appendix Applications to Switching Theory
Pages 539-549
References
Pages 551-574
Author Index
Pages 575-577
Subject Index
Pages 579-583
