On pseudo-BCK algebras with pseudo-double negation

Abstract

A special class of pseudo-BCK algebras is that of the pseudo-BCK algebras with pseudo-double negation which generalize  some particular structures, such as pseudo-MV algebras. The aim of this paper is to present some new properties of the pseudo-BCK algebras with pseudo-double negation. As main results, we prove some conditions for a pseudo-BCK lattice with pseudo-double negation to be distributive and we present equivalent definitions for pseudo-BCK algebras with pseudo-double negation.