Title:
 A logic for rough sets

Author:

Ivo Düntsch ,
Dept of Computer Science ,
Brock University ,
St Catherines, Ontario, L2S 3A1, Canada

Status:
 Theoretical Computer Science (B) 179 (1997), 427  436

Abstract:

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, cf. Pomykala & 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 Katrinák (1974), we present such a
logic for rough sets and its algebraic semantics in the spirit of
Andréka, Németi, and Sain.
