Title: Many-valued tableau calculi for decision logic based on approximation regions in VPRS

Authors: Yotaro Nakayama; Seiki Akama; Tetsuya Murai

Addresses: Technology Research and Innovation, Nihon Unisys, Ltd., 1-1-1 Toyosu, Tokyo 135-8560, Japan ' C-Republic, Inc., 1-20-1 Higashi-Yurigaoka, Kawasaki 215-0012, Japan ' Chitose Institute of Science and Technology, 758-65 Bibi, Chitose 066-865, Japan

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.

Keywords: many-valued logic? tableau calculi? decision logic? variable precision rough set? VPRS? knowledge representation.

DOI: 10.1504/IJRIS.2021.10041247

International Journal of Reasoning-based Intelligent Systems, 2021 Vol.13 No.4, pp.235 - 242

Accepted: 22 Oct 2020
Published online: 30 Oct 2021 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article