Rough Sets Through Algebraic Logic

While studying rough equality within the framework of the modal system S 5, an algebraic structure called rough algebra [1], came up. Its features were abstracted to yield a topological quasi-Boolean algebra (tqBa). In this paper, it is observed that rough algebra is more structured than a tqBa. Thus, enriching the tqBa with additional axioms, two more structures, viz. pre-rough algebra and rough algebra, are denned. Representation theorems of these algebras are also obtained. Further, the corresponding logical systems L 1 L 2 are proposed and eventually, L 2 is proved to be sound and complete with respect to a rough set semantics.

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