The notions of BCK-algebras and BCI-algebras was first introduced by Imai and Iseki in 1966. It was originated from two different ways: One of them is based on set theory; another is from classical and non-classical propositional calculi. As is well known, there is a close relationship between the notions of the set difference in set theory and the implications in logical systems. In this paper, efforts are intensified to consider BCI-algebra as a class of logical algebras which are the algebraic formulations of the set difference together with its properties. In the process, some fundamental properties of subtraction algebra will be considered and the goal is to present subtraction algebras as typical examples of BCI-algebra