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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 ...
A note on chain-based semi-Heyting algebras
(Wiley VCH Verlag, 2020-12)
We determine the number of non-isomorphic semi-Heyting algebras on an n-element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. ...
Semi-Heyting Algebras and Identities of Associative Type
(University of Lodz, 2019-06-30)
An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. ℋ denotes the ...
Localization of semi-Heyting algebras
(University of Craiova, 2016-12)
In this note, we introduce the notion of ideal on semi-Heyting algebras which allows us to consider a topology on them. Besides, we define the concept of F−multiplier, where F is a topology on a semi-Heyting algebra L, ...
Semi-intuitionistic Logic
(Springer, 2011-07-18)
The purpose of this paper is to define a new logic SI called semi-intuitionistic logic such that the semi-Heyting algebras introduced in [4] by Sankappanavar are the semantics for SI. Besides, the intuitionistic logic will ...
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 ...
On some semi-intuitionistic logics
(Instituto de Matemática de Bahía Blanca, 2015)
Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which weredefined by H. P. Sankappanavar in [3] as a variety generalizing the one of Heyting algebraswhile retaining some important features, ...
On Some Semi-Intuitionistic Logics
(Springer, 2015-04-05)
Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for ...