Characterization theorem of lattice implication algebras

Abstract

In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication algebras coincides with the class of all bounded commutative BCK-algebras. Hence lattice implication algebras are categorically equivalent to MV-algebras and to Wajsberg algebras.