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 [24]. 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 Katriňák [16], we present such a logic for rough sets and its algebraic semantics in the spirit of Andréka et al [2]. keywords: Rough sets, algebraic semantics, regular double Stone algebras