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Monadic k x j-rough Heyting algebras
(Springer, 2021-11-13)
In this paper, we introduce the variety of algebras, which we call monadic kxj-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in 3x2 case they coincide with monadic 3-valued ...
A Topological Duality for k x j-rough Heyting Algebras
(Old City Publishing Inc, 2020-08)
k-rough Heyting algebras were introduced by Eric San Juan as an algebraic formalism for reasoning on finite increasing sequences over Boolean algebras in general and on generalizations of rough set concepts in particular. ...
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 ...
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]. ...
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 ...
Free-decomposability in varieties of semi-Heyting algebras
(Wiley VCH Verlag, 2012-05)
In this paper we prove that the free algebras in a subvariety V of the variety SH of semi-Heyting algebras are directly decomposable if and only if V satisfies the Stone identity.
A categorical equivalence between semi-Heyting algebras and centered semi-Nelson algebras
(Oxford University Press, 2018-08)
Motivated by a construction due to R. Cignoli that relates Heyting algebras and centered Nelson algebras, in this paper we prove that there exists an equivalence between the category of semi-Heyting algebras and the category ...
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 ...
A categorial equivalence for semi-Nelson algebras
(Springer, 2021-09-13)
We present a category equivalent to that of semi-Nelson algebras. The objects in this category are pairs consisting of a semi-Heyting algebra and one of its filters. The filters must contain all the dense elements of the ...