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The Semi-Heyting Brouwer Logic
(Springer, 2015-08)
In this paper we introduce a logic that we name semi Heyting–Brouwer logic, SHB, in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, ...
Semi-Heyting Algebras Term-equivalent to Gödel Algebras
(Springer, 2013-07)
In this paper we investigate those subvarieties of the variety SH of semi-Heyting algebras which are term-equivalent to the variety LH of Gödel algebras (linear Heyting algebras). We prove that the only other subvarieties ...
Semi-Nelson Algebras
(Springer, 2016-11)
Generalizing the well known and exploited relation between Heyting and Nelson algebras to semi-Heyting algebras, we introduce the variety of semi-Nelson algebras. The main tool for its study is the construction given by ...
Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic
(Springer, 2016-12)
The variety SH of semi-Heyting algebras was introduced by H. P. Sankappanavar (in: Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress, Universidad Nacional del Sur, Bahía Blanca, 2008) [13] as an abstraction of ...
The finite model property for the variety of Heyting algebras with successor
(Unión Matemática Argentina, 2012-06)
The finite model property of the variety of S-algebras was proved by X. Caicedo using Kripke model techniques of the associated calculus. A more algebraic proof, but still strongly based on Kripke model ideas, was given ...
On products of posets and coproducts of KM-algebras
(Springer Verlag Berlín, 2015-10)
The main goal of this work is to give an explicit computation of some coproducts in the variety of KM-algebras introduced by the Chişinǎu group headed by Kuznetsov during the decade of the 1970s. This is done using a ...
A note on ℋ3-algebras
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 1997)
In this note we shall generalize some results of the threevalued Lukasiewicz algebras to three-valued symmetrical Heyting algebras. We prove that a three-valued Heyting algebra with axe is a product of a Boolean algebra ...
On frontal operators in Hilbert algebras
(Oxford University Press, 2015-03)
In this article, we introduce and study a family of compatible functions in Hilbert algebras which in the case of Heyting algebras agree with the frontal operators given by Esakia (2006, J. Appl. Non-Class. Log., 16, ...
A Note on Hilbert Algebras and Their Related Generalized Esakia Spaces
(Springer, 2016-11)
Generalized Esakia spaces are the topological duals of bounded implicative semilattices in the duality studied by G. Bezhanishvili and R. Jansana. We study the relation between a Hilbert algebra and the generalized Esakia ...
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 ...