A LOGIC FOR ROUGH SETS

The collection of all subsets of a set forms a Boolean algebra under t he 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 p ropositional logic are Boolean algebras, and it is reasonable to assum e that regular double Stone algebras are a class of algebras appropria te for a logic of rough sets. Using the representation theorem for the se algebras by Katrinak (1974), we present such a logic for rough sets and its algebraic semantics in the spirit of Andreka and Nemeti (1994 ).