Lukasiewicz-Moisil Algebras (Annals of Discrete Mathematics)

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. 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 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.

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