Relation between Hilbert Algebras and BE-Algebras
Akbar Rezaei, Arsham Borumand Saeid, R. A. Borzooei, Shahid Bahonar · 2013
Hilbert algebras are introduced for investigations in intuitionistic and other non - classical logics and BE -algebra is a generalization of dual BCK -algebra. In this paper, we investigate the relationship between Hilbert algebras and BE -algebras. In fact, we show that a commutative implicative BE -algebra is equivalent to the commutative self distributive BE -algebra, therefore Hilbert algebras and commutative self distributive BE -algebras are equivalent.