A logic for rough sets

The collection of all subsets of a set forms a Boolean algebra under the usual set-theoretic operations, while the collection of rough sets of an approximation space is a regular double Stone algebra (Pomykala and Pomykala, 1988). The appropriate class of algebras for classical propositional logic are Boolean algebras, and it is reasonable to assume that regular double Stone algebras are a class of algebras appropriate for a logic of rough sets. Using the representation theorem for these algebras by Katrinak (1974), we present such a logic for rough sets and its algebraic semantics in the spirit of Andreka and Nemeti (1994).