Affiliations: Machine Intelligence Unit, Indian Statistical Institute, 203, B. T. Road, Calcutta 700 035, India. miux9503@isical.ernet.in | Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Calcutta 700 019, India. itbpc@gems.vsnl.net.in
Abstract: While studying rough equality within the framework of the modal system S5, 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 ℒ1 ℒ2 are proposed and eventually, ℒ2 is proved to be sound and complete with respect to a rough set semantics.
Keywords: Rough set theory, Algebraic logic, Modal system S 5
