Ordered algebras such as Boolean algebras, Heyting algebras, lattice-ordered groups, and
MV-algebras have long played a decisive role in logic, although perhaps only in recent …

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We develop a general algebraic and proof-theoretic study of substructural logics that may
lack associativity, along with other structural rules. Our study extends existing work on …

The last decade has seen an enormous development in infinite-valued systems and in
particular in such systems which have become known as mathematical fuzzy logics. The …

Continuing with our general study of algebraic hyperstructures, we focus on the residuated
operation in the framework of multilattices. Firstly, we recall the existing relation between …

In this paper we review some of the main achievements of the semiring-theoretic approach
to MV-algebras initiated and pursued mainly by the present authors and their collaborators …

In this paper, we investigate some properties of nuclei and conuclei on residuated lattices
and their concrete structures. By means of nuclei and conuclei we give the respective …

Actually it is a well accepted fact that fuzzy set theory, as a mathematical theory of a sort of
generalized sets, has a natural relationship to particular kinds of non-classical logics of …

Starting from an arbitrary MTL-chain, two constructions are considered: the MacNeille
completion of the underlying order with suitable extensions of the other operations, and a …

A residuated ordered algebra is a partially ordered set with additional
'residuated'operations. A construction is presented that, from any partial subalgebra of a …