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The subvariety of commutative residuated lattices represented by twist-products
(Springer, 2014-03)
Given an integral commutative residuated lattice L, the product L × L can be endowed with the structure of a commutative residuated lattice with involution that we call a twist-product. In the present paper, we study the ...
Varieties of K-lattices
(Elsevier, 2021-08)
In this paper we deal with varieties of commutative residuated lattices that arise from a specific kind of construction: the twist-product of a lattice. Twist-products were first considered by Kalman in 1958 to deal with ...
Compatible operations on commutative weak residuated lattices
(Springer, 2015-04)
Compatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this ...
Regular elements and Kolmogorov translation in residuated lattices
(Springer, 2015-02)
In this article we study in detail the regular elements of a bounded, commutative and integral residuated lattice. We introduce the notion of a regular variety and explore its relationship with the Kolmogorov negative ...
On Principal Congruences in Distributive Lattices with a Commutative Monoidal Operation and an Implication
(Springer, 2019-04-12)
In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal ...
Remarks on an algebraic semantics for paraconsistent Nelson's logic
(Universidade Estadual de Campinas. Centro de Lógica, Epistemologia e História da Ciência, 2011-03)
In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson's logic. In the present paper ...
A representation theorem for integral rigs and its applications to residuated lattices
(Elsevier Science, 2016-05)
We generalize the Dubuc–Poveda representation theorem for MV-algebras so that it applies to other algebraic categories of residuated join-semilattices. In particular, as a corollary, we obtain a representation result for ...
Constructible sets in lattice-valued models
(Universidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá, 2023)
We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s
work on Intuitionistic Kripke models of Set Theory.
Firstly, we consider constructable sets within valued models of Set Theory. ...