ON HEYTING ALGEBRAS AND DUAL BCK-ALGEBRAS

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.