In this paper we overview basic known results about the varieties generated by De Morgan triples and about the problem to find equations defining the variety generated by a concrete De Morgan triple. We also provide some alternative proofs and some new results, specially for the case of Łukasiewicz De Morgan triples.

this paper is the first of a two part series. in this paper, we first prove that the variety of dually quasi-de morgan stone semi-heyting algebras of level 1 satisfies the strongly blended $lor$-de morgan law introduced in cite{sa12}. then, using this result and the results of cite{sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

this paper is the second of a two part series. in this part, we prove, using the description of simples obtained in part i, that the variety $mathbf{rdqdstsh_1}$ of regular dually quasi-de morgan stone semi-heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{rdqdstsh_1}$-chains and the variety of dually quasi-de morgan boolean semi-heyting algebras--...

This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--...

We provide a complete classification of solvable instances of the equational unification problem over De Morgan and Kleene algebras with respect to unification type. The key tool is a combinatorial characterization of finitely generated projective De Morgan and Kleene algebras.

Most normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve either tautologies or contradictions which are fundamental for automatic theorem provers based on refutation methods. De Morgan implicative systems are triples like the De Morgan system, but considering fuzzy implications instead of t-conorms. These s...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...