L. C. Ciungu - Department of Mathematics, University of Iowa, ۱۴ MacLean Hall, Iowa City, Iowa ۵۲۲۴۲-۱۴۱۹, USA
A. Borumand Saeid - Department of Pure Mathematics, Faculty of Math. & Comput., Shahid Bahonar University of Kerman, Kerman, Iran
A. Rezaei - Department of Mathematics, Payame Noor University, P.O.Box. ۱۹۳۹۵-۳۶۹۷, Tehran, Iran

In this paper, we define and study the modal operators on pseudo-BE algebras as special cases of closure operators on these structures.We prove that the composition of two modal operators is a modal operator if and only if they commute.For the particular case of a good pseudo-BCK algebra an equivalent definition of the modal operators is given, and the notion of a strong modal operator is introduced and studied.We also define the notions of modal deductive systems and modal homomorphisms on pseudo-BE algebras and we investigate their properties. It is proved that, if two modal operators have the same image, then they coincide.Also, given a normal modal deductive system H of a distributive modal pseudo-BE algebra (A,f) we construct a modal operator on the quotient pseudo-BE algebra A/H.

Non-classical logic, pseudo-BE algebra, Modal operator, strong modal operator, modal deductive system, modal homomorphism