Sequent calculus system for rough sets based on rough Stone algebras

Many researchers study rough sets from the point of description of the rough set pairs (a rough set pair is also called a rough set), i.e., . An important result is that the collection of rough sets of an approximation space can be made into a Stone algebra. The collection of all subsets of a set forms a Boolean algebra under the usual set theoretic operations, a model for classical proposition logic are Boolean algebras. So, it is reasonable to assume that rough Stone algebras form a class of algebras appropriate for a logic of rough sets. In this paper, a sequent calculus system corresponding to rough Stone algebra, is proposed. The syntax and semantics are defined. The soundless and completeness are proved.