A note on definability and approximations

Abstract. Definability and approximations are two important notions of the theory of rough sets. In many studies, one is used to define the other. There is a lack of an explicit interpretation of the physical meaning of definability. In this paper, the definability is used as a more primitive notion, interpreted in terms of formulas of a logic language. A set is definable if there is a formula that defines the set, i.e., the set consists of all those elements satisfying the formula. As a derived notion, the lower and upper approximations of a set are two definable sets that approximate the set from below and above, respectively. This formulation may be more natural, bringing new insights into our understanding of rough set approximations.