Lukasiewicz-Moisil AlgebrasThe 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. |
Contents
| 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 |
| 551 | |
| 575 | |
| 579 | |
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Common terms and phrases
9-filter a e C(L a e F a s y analytic tableau axioms bijection Boicescu Boolean algebra Cignoli complete complete lattice conditions are equivalent congruence Corollary CT(X Dedº F defined Definition denote distributive lattice Ds(L dual element endomorphisms epimorphism exists finite following conditions functor hence Heyting algebra homomorphism implies injective involution isomorphism k-consistent Lemma LM-algebra logic Lukasiewicz algebras Lukasiewicz-Moisil algebras m-complete Math maximal monadic Boolean algebras monomorphism Monteiro Morgan algebra morphism morphism f n-valued Moisil algebra n-valued Post algebra negation Notation obtain operations polyadic Ú-algebra poset Priestley space prime filter Proof Prop(V properties Proposition propositional calculus prove Remark satisfies se:S semilattice Spec Stone algebra subalgebra subdirect product subset Suppose surjective T-algebra Theorem three-valued Tºp unique