An overview of hyper logical algebras

Hyper logical algebras were rst studied in 2000 by Bor- zooei et al. They applied the concept of hyperstruc- tures to one of the logical algebraic structures known as the BCK-algebra, and introduced two generalizations of them called the hyper BCK-algebra and hyper K-algebra. Then many researchers in this eld continued their re- search and used hyperstructures on other logical alge- bras and introduced the concepts of hyper residuated lattices, hyper BL-algebras, hyper MV-algebras, hyper EQ-algebras, hyper BE-algebras, hyper equality algebras, hyper hoops and etc. Moreover, they dened some new notions such as different kinds of hyper ideals, hyper l- ters and hyper congruence relations on these structures and studied some properties, the relation among them and the quotient structure. Now, in this paper, we review the denitions of all those hyper logical algebras and investigate relations among them.