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Epimorphisms between finite MV-algebras

Aldo V. Figallo;  Marina B. Lattanzi — 2017

Mathematica Bohemica

MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras A and B . Specifically, we define the mv-functions with domain in...

Free Modal Pseudocomplemented De Morgan Algebras

Aldo V. Figallo;  Nora Oliva;  Alicia Ziliani — 2018

Bulletin of the Section of Logic

Modal pseudocomplemented De Morgan algebras (or mpM-algebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1 (2014), pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ(∼x)* = (∼(xΛ(∼x)*))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new characterizations...

A Topological Approach to Tense LMn×m-Algebras

Aldo V. Figallo;  Inés Pascual;  Gustavo Pelaitay — 2020

Bulletin of the Section of Logic

In 2015, tense n × m-valued Lukasiewicz–Moisil algebras (or tense LMn×m-algebras) were introduced by A. V. Figallo and G. Pelaitay as an generalization of tense n-valued Łukasiewicz–Moisil algebras. In this paper we continue the study of tense LMn×m-algebras. More precisely, we determine a Priestley-style duality for these algebras. This duality enables us not only to describe the tense LMn×m-congruences on a tense LMn×m-algebra, but also to characterize the simple and subdirectly irreducible tense...

Modal Pseudocomplemented De Morgan Algebras

Aldo V. Figallo;  Nora Oliva;  Alicia Ziliani — 2014

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Modal pseudocomplemented De Morgan algebras (or m p M -algebras for short) are investigated in this paper. This new equational class of algebras was introduced by A. V. Figallo and P. Landini ([Figallo, A. V., Landini, P.: Notes on 4 -valued modal algebras Preprints del Instituto de Ciencias Básicas, Univ. Nac. de San Juan 1 (1990), 28–37.]) and they constitute a proper subvariety of the variety of all pseudocomplemented De Morgan algebras satisfying x ∧ ( ∼ x ) * = ( ∼ ( x ∧ ( ∼ x ) * ) ) * . Firstly, a topological duality for these algebras...

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