6 citations · 16 across the 15 of their papers we have counts for
21 papers
Connexive logics and connexive semi-Heyting algebras
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
In this paper, we define and investigate a connexive logic, called 'Connexive semi-Heyting logic' (\mathcal{CSH} for short) and a new subvariety CSH of the variety SH of semi-Heyti…
Unorthodox Algebras and their associated Unorthodox Logics
Hanamantagouda P. Sankappanavar
This paper grew out of our investigation into a simple, but natural, question: Can 'F implies T' be distinct from F and T? To this end, we introduce five 'unorthodox' algebras that…
Johnson's axioms revisited: Bases for Boolean algebras containing identities of associative type. I
Hanamantagouda P. Sankappanavar
This paper is inspired by 1892 paper of Johnson, where he has given an axiomatization for the variety of Boolean algebras (equivalently, for classical propositional calculus). The…
Amalgamation Property in the subvarieties of Gautama and Almost Gautama algebras
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
Gautama algebras were introduced recently, as a common generalization of regular double Stone algebras and regular Kleene Stone algebras. Even more recently, Gautama algebras were…
Regular Double -Algebras: A converse to a Katriňák's Theorem, and Applications
Juan M. Cornejo, Michael Kinyon, Hanamantagouda P. Sankappanavar
In 1973, Katriňák proved that regular double -algebras can be regarded as (regular) double Heyting algebras by ingeniously constructing binary terms for the Heying implication a…
Semidistributivity and Whitman Property in Implication Zroupoids
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
In 2012, the second author introduced and studied the variety of implication zroupoids that generalize De Morgan algebras and -semilattices with . An algebra…
Implication Zroupoids and Birkhoff Systems
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
An algebra , where is binary and is a constant, is called an implication zroupoid (I-zroupoid, for short) if A satisfies the identities: $(…
Varieties of Regular Pseudocomplemented de Morgan Algebras
M. E. Adams, H. P. Sankappanavar, Júlia Vaz de Carvalho
In this paper, we investigate the varieties and of regular pseudocomplemented de Morgan and Kleene algebras of range , respectively. Priestley dualit…
A Logic for Dually Hemimorphic Semi-Heyting Algebras and its Axiomatic Extensions
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
In this paper, we focus on the variety DHMSH of dually hemimorphic semi-Heyting algebras from a logical point of view. Firstly, we present a Hilbert-style axiomatization of a new l…
The lattice of varieties of implication semigroups
S. V. Gusev, H. P. Sankappanavar, B. M. Vernikov
In 2012, the second author introduced and examined a new type of algebras as a generalization of De Morgan algebras. These algebras are of type (2,0) with one binary and one nullar…
De Morgan Semi-Heyting and Heyting Algebras
Hanamantagouda P. Sankappanavar
The variety DMSH of semi-Heyting algebras with a De Morgan negation was introduced in [12] and an increasing sequence DMSHn of level n, n being a natural number, of its subvarietie…
Symmetric implication zroupoids and identities of Bol-Moufang type
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
An algebra , where is binary and is a constant, is called an implication zroupoid (-zroupoid, for short) if …
Implication Zroupoids and Identities of Associative Type
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
An algebra , where is binary and is a constant, is called an implication zroupoid (-zroupoid, for short) if …
Symmetric Implication Zroupoids and Weak Associative Laws
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
An algebra , where is binary and is a constant, is called an implication zroupoid (-zroupoid, for short) if …
JI-distributive, dually quasi-De Morgan semi-Heyting and Heyting algebras
Hanamantagouda P. Sankappanavar
The variety DQD of semi-Heyting algebras with a weak negation, called dually quasi-De Morgan operation, and several of its subvarieties were investigated in a series of four papers…
Order in Implication Zroupoids
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
The variety of implication zroupoids was defined and investigated by Sankappanavar ([7]) as a generalization of De Morgan algebras. Also, in [7], several new subvariet…
Semisimple Varieties of Implication Zroupoids
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
It is a well known fact that Boolean algebras can be defined using only implication and a constant. In 2012, this result was extended to De Morgan algebras in [8] which led Sankapp…
On Implicator Groupoids
Juan M. Cornejo, Hanamantagouda P. Sankappanavar
In a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras-this…
Boole's Principles of Symbolical Reasoning
Stanley Burris, H. P. Sankappanavar
In modern algebra it is well-known that one cannot, in general, apply ordinary equational reasoning when dealing with partial algebras. However Boole did not know this, and he took…
A note on regular De Morgan semi-Heyting algebras
Hanamantagouda P. Sankappanavar
The purpose of this note is two-fold. Firstly, we prove that the variety RDMSH1 of regular De Morgan semi-Heyting algebras of level 1 satisfies Stone identity and present (equation…
Boole's Method I. A Modern Version
Stanley Burris, H. P. Sankappanavar
A rigorous, modern version of Boole's algebra of logic is presented, based partly on the 1890s treatment of Ernst Schroder.