This article deals with many-valued modal logics, based only on the necessity operator, over
a residuated lattice. We focus on three basic classes, according to the accessibility relation …

This paper is part of a general project of developing a systematic and algebraic proof theory
for nonclassical logics. Generalizing our previous work on intuitionistic-substructural axioms …

We continue our program of establishing connections between proof-theoretic and order-
algebraic properties in the setting of substructural logics and residuated lattices. Extending …

We show that a large number of equations are preserved by Dedekind-MacNeille
completions when applied to subdirectly irreducible FL-algebras/residuated lattices. These …

The paper studies the weak Grzegorczyk logic w Grz. In particular, we discuss the
relationship between Grz, GL and w Grz as an interesting example of the relationship …

Ordered algebraic structures are encountered in many areas of mathematics. One frequently
wishes to embed a given ordered algebraic structure into a complete ordered algebraic …

In view of traditional PID controller parameters optimization by ZN method, and none
satisfactory dynamic properties can be gotten, so a new PID controller parameters …

We prove that every subvariety of BL-algebras which is not finitely generated is not σ-
canonical. We also prove π-canonicity for an infinite family of subvarieties of BL-algebras …

Discrete dualities are developed for n-potent MTL-algebras and for 2-potent BL-algebras.
That is, classes of frames, or relational systems, are defined that serve as dual counterparts …

Abstract Based on Alasdair Urquhart's representation of not necessarily distributive bounded
lattices we exhibit several discrete dualities in the spirit of the “duality via truth” concept by …