Implicative commutative semigroups are equivalent to a class of BCK algebras.
Implicative hyper -algebras
In this note we first define the notions of (weak, strong) implicative hyper -algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper -ideals. Also we obtain some relations between these notions and (weak) implicative hyper -ideals. Finally, we study the implicative hyper -algebras of order 3, in particular we obtain a relationship between the positive implicative...
Implicative ideals of BCK-algebras based on the fuzzy sets and the theory of falling shadows.
In memory of Jaroslav Ježek
Independence in -groups
Independent axiomatization of varieties of lattice ordered groups
Information frames, implication systems and modalities.
We investigate the logical systems which result from introducing the modalities L and M into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Our results lead to the formulation of a uniform labelled refutation system for these logics.
Inner product in -groups
Integral Domain Type Representations in Sheaves and Other Topoi.
Integral extension procedures in weakly σ-complete lattice-ordered groups, II
Integral extension procedures in weakly σ-complete lattice-ordered groups, I
Integrally ordered semigroups.
Integrals on lattice-ordered groups
Interior and closure operators on bounded commutative residuated l-monoids
Topological Boolean algebras are generalizations of topological spaces defined by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Łukasiewicz infinite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative Rl-monoids that contains e.g. the classes of BL-algebras...
Interior and closure operators on bounded residuated lattices
Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated...
Interior and closure operators on bounded residuated lattice ordered monoids
-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior -algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on -monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on -algebras.
Interior and Closure Operators on Commutative Bounded Residuated Lattices
Commutative bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate additive closure and multiplicative interior operators on this class of algebras.
Interval-Valued Fuzzy Ideals Generated by an Interval-Valued Fuzzy Subset in Ordered Semigroups.
Intuitionistic fuzzy ideals of BCK-algebras.
Invariant sets in the group of isometries of a lattice-ordered group.
This paper deals with the invariant sets in the group of isometries of a lattice-ordered group. It is shown that all the invariant sets are union of some transitivity subsets of the spheres.