Many-valued tableau calculi for decision logic based on approximation regions in VPRS
by Yotaro Nakayama; Seiki Akama; Tetsuya Murai
International Journal of Reasoning-based Intelligent Systems (IJRIS), Vol. 13, No. 4, 2021

Abstract: Rough sets theory is studied to manage uncertain and inconsistent information. While the Pawlak's decision logic of rough sets is based on classical two-valued logic, this causes inconvenience for the various reasoning. In this paper, we propose many-valued logics, especially a three-valued logic, as the deduction system for the decision logic of rough sets. To enhance the decision logic from classical bivalent logic to three-valued logic, we adopt variable precision rough set (VPRS). As a deductive basis for three-valued decision logic, we define a consequence relation based on three-valued semantics to constructing a deduction system with the semantic tableau. We show to deal with two types of the third value of three-valued semantics one is unknown, and the other is inconsistent using Belnap's four-valued interpretation.

Online publication date: Sat, 30-Oct-2021

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