This paper is concerned with some issues connected with the foundations of rough set theory. Particularly the problem of definition of a rough set is discussed.
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In this paper, we study indiscernibility relations and complementarity relations in information systems. The first-order characterization of indiscernibility and complementarity is obtained through a duality result between information systems and certain structures of relational type characterized by first-order conditions. The modal analysis of indiscernibility and complementarity is performed through a modal logic which modalities correspond to indiscernibility relations and complementarity relations in information systems.
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