On Heyting algebras and dual BCK-algebras

Document Type: Research Paper

Authors

1 Mokwon University

2 Chungju National University

Abstract

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equivalent to an $i$-invariant and $m$-invariant dual $BCK$-semilattices, and show that a commutative Heyting algebra is equivalent to a bounded implicative dual $BCK$-algebra.

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