This paper investigates some basic properties of covering generalized rough sets, and

their comparison with the corresponding ones of Pawlak s rough sets, a tool for data

mining. The focus here is on the concepts and conditions for two coverings to generate

the same covering lower approximation or the same covering upper approximation. The

concept of reducts of coverings is introduced and the procedure to find a reduct for a

covering is given. It has been proved that the reduct of a covering is the minimal

covering that generates the same covering lower approximation or the same covering

upper approximation, so this concept is also a technique to get rid of redundancy in

data mining. Furthermore, it has been shown that covering lower and upper approximations

determine each other. Finally, a set of axioms is constructed to characterize the

covering lower approximation operation.