Reasoning about Covering-based Rough Sets Using Three Truth Values.

The paper presents a natural three-valued logic for reasoning about coveringbased 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.

Authors

• Beata Konikowska
• Arnon Avron

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