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.

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