Cantor-Bernstein theorem for -algebras
Classes of filters in generalizations of commutative fuzzy structures
Bounded commutative residuated lattice ordered monoids (-monoids) are a common generalization of -algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative -monoids.
Classes of fuzzy filters of residuated lattice ordered monoids
The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of -algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding...
Commutative directoids with sectional involutions
The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.
Commutative directoids with sectionally antitone bijections
We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.
Completion closed algebras and models of Peano arithmetic
Complicated BE-algebras and characterizations of ideals
In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive and complicated BE-algebra, characterizations of ideals are obtained.
Convergences in Perfect BL-algebras.
Corrigendum à l'article "Sur la construction de certaines MS-algèbres" (Port. Math., 39(1-4) (1980), 489-496)
Curry algebras
In [6] da Costa has introduced a new hierarchy , of logics that are both paraconsistent and paracomplete. Such logics are now known as non-alethic logics. In this article we present an algebraic version of the logics and study some of their properties.
Cyclic ordered groups and MV-algebras