The representation of human-originated information and the formalization of commonsense
reasoning has motivated different schools of research in Artificial or Computational …

The main goal of this paper is to investigate derivations in residuated lattices and
characterize some special types of residuated lattices in terms of derivations. In the paper …

Substructural logics have received a lot of attention in recent years from the communities of
both logic and algebra. We discuss the algebraization of substructural logics over the full …

The commutative residuated lattices were first introduced by M. Ward and RP Dilworth as
generalization of ideal lattices of rings. Non-commutative residuated lattices, called …

In this paper, the notion of minimal prime ideal is introduced in residuated lattices and
related properties are investigated. Also, new equivalent characterizations and properties for …

The goal of this two-part series of papers is to show that constructive logic with strong
negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the …

In the paper, we introduce the notion of state operators on residuated lattices and investigate
some related properties of such operators. Also, we give characterizations of Rl-monoids …

Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short),
can be considered as a substructural logic. We use algebraic tools developed to study …

The classical Glivenko theorem asserts that a propositional formula admits a classical proof
if and only if its double negation admits an intuitionistic proof. By a natural expansion of the …

The aim of this paper is to give a description of the free algebras in some varieties of
Glivenko MTL-algebras having the Boolean retraction property. This description is given …