Rough Sets and 3-Valued Logics

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Rough Sets and 3-Valued Logics
In the paper we explore the idea of describing Pawlak's rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f -- to the negative region, and the undefined value u -- to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the value t is treated as designated, the above logic is a "common denominator" for Kleene and Lukasiewicz 3-valued logics, which represent its two different "determinizations". In turn, the weak semantics -- where both t and u are treated as designated -represents such a "common denominator" for two major 3-valued paraconsistent logics. We give sound and complete, cut-free sequent calculi for both versions of the logic generated by the rough set Nmatrix. Then we derive from these calculi sequent calculi with the same pro...
Arnon Avron, Beata Konikowska
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Authors Arnon Avron, Beata Konikowska
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