Reasoning about covering-based rough sets using three truth values

The paper presents a natural three-valued logic for reasoning about covering-based rough sets. Atomic formulas of the logic represent membership of objects of the universe in rough sets, and complex formulas are built out of the atomic ones using three-valued Kleene connectives. To reflect the structure of rough sets, semantics of the logic employs three truth values: t — representing truth and corresponding to membership of an object in the positive region of a set, f — representing falsity and corresponding to membership in the negative region, and u — representing undefinedness (lack of information) and corresponding to membership in the boundary region of the set. In the paper we provide a finitely strongly sound and complete Gentzen-style sequent calculus for the described logic.