On Rough Quantiiers

Rough set theory is proposed as the theoretical foundation of information systems and has found rapidly growing applications in intelligent data analysis. An especially interesting problem is its relationship with other knowledge representation formalisms. The most well-known result is that it can provide a semantics for modal logics. Motivated by the strong analogy between quantiiers and modal operators, we would like to consider the generalization of universal and existential quantiiers in rst order logic based on rough set notions. By viewing the set of variable assignments as the universe of the approximation space, we can present some quantii-cational logics based on rough set theory in a uniform way.