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Displaying 1 – 20 of 74

A Cantor-Bernstein theorem for $σ$ -complete MV-algebras

Anna de Simone, Daniele Mundici, Mirko Navara (2003)

Czechoslovak Mathematical Journal

The Cantor-Bernstein theorem was extended to $σ$ -complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to $σ$ -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.

A constructive proof that every 3-generated l-group is ultrasimplicial

Daniele Mundici, Giovanni Panti (1999)

Banach Center Publications

We discuss the ultrasimplicial property of lattice-ordered abelian groups and their associated MV-algebras. We give a constructive proof of the fact that every lattice-ordered abelian group generated by three elements is ultrasimplicial.

A duality between unary algebras and their subuniverse lattices

Bordalo, G. (1989)

Portugaliae mathematica

A note on congruence systems of MS-algebras

M. Campercholi, Diego Vaggione (2007)

Mathematica Bohemica

Let $L$ be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences $(θ_{1}, ..., θ_{n}; x_{1}, ..., x_{n})$ in $L$ can be reduced to solving the restriction of the system to the skeleton of $L$ , plus solving the restrictions of the system to the intervals $[x_{1}, {\bar{\bar{x}}}_{1}], \dots, [x_{n}, {\bar{\bar{x}}}_{n}] .$

A Note on Pseudo-Kleene Algebras

Ivan Chajda (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members.

A note on the symmetric difference in lattices.

Eloy Renedo, Enric Trillas, Claudio Alsina (2005)

Mathware and Soft Computing

The paper introduces a definition of symmetric difference in lattices with negation, presents its general properties and studies those that are typical of ortholattices, orthomodular lattices, De Morgan and Boolean algebras.

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras...

A short note on lattices allowing disjunctive reasoning.

Enric Trillas, Eloy Renedo, Claudi Alsina (2006)

Mathware and Soft Computing

This short note shows that the scheme of disjunctive reasoning, a or b, not b : a, does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality b' · (a+b) ≤ a, forces the structure to be a boolean algebra.

Affine complete algebras abstracting Kleene and Stone algebras.

Haviar, M. (1993)

Acta Mathematica Universitatis Comenianae. New Series

Affine completeness of de Morgan algebras

Vladimir Kuchmei (2002)

Mathematica Slovaca

Algebre di Łukasiewicz quasi-locali Stoneane

Francesco Lacava (2001)

Bollettino dell'Unione Matematica Italiana

We prove some properties of quasi-local Ł-algebras. These properties allow us to give a structure theorem for Stonean quasi-local Ł-algebras. With this characterization we are able to exhibit an example which provides a negative answer to the first problem posed in [4].

An algebraic completeness proof for Kleene's 3-valued logic

Maurizio Negri (2002)

Bollettino dell'Unione Matematica Italiana

We introduce Kleene's 3-valued logic in a language containing, besides the Boolean connectives, a constant $n$ for the undefined truth value, so in developing semantics we can switch from the usual treatment based on DM-algebras to the narrower class of DMF-algebras (De Morgan algebras with a single fixed point for negation). A sequent calculus for Kleene's logic is introduced and proved complete with respect to threevalent semantics. The completeness proof is based on a version of the prime ideal...

Classification of the regular De Morgan algebras of fuzzy sets.

Francesc Esteva, Núria Piera (1984)

Stochastica

A characterization of regular lattices of fuzzy sets and their isomorphisms is given in Part I. A characterization of involutions on regular lattices of fuzzy sets and the isomorphisms of De Morgan algebras of fuzzy sets is given in Part II. Finally all classes of De Morgan algebras of fuzzy sets with respect to isomorphisms are completely described.

Closure Łukasiewicz algebras

Abad Manuel, Cimadamore Cecilia, Díaz Varela José, Rueda Laura, Suardíaz Ana (2005)

Open Mathematics

In this paper, the variety of closure n-valued Łukasiewicz algebras, that is, Łukasiewicz algebras of order n endowed with a closure operator, is investigated. The lattice of subvarieties in the particular case in which the open elements form a three-valued Heyting algebra is obtained.

Currently displaying 1 – 20 of 74