Natural Deduction for Three-valued Logic Based on Rough Set Logic

Abstract

Duntsch has proposed the rough set logic for the regular double stone algebra. Then, there have been many studies on the logical system based on rough set logic, however, the characteristics of the deductive system of rough set logic have not been investigated enough. In this paper, we show that we can construct a natural deduction system K3RSL for strong Kleene’s three-valued logic, which is based on the algebraic semantics with rough set logic. For this, we have provided the interpretation of consequence relation with the semantic function of rough set logic and have shown the sketch of the soundness and completeness theorem.