Graded Many-Valued Modal Logic and Its Graded Rough Truth

Abstract

Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses the graded modal logic and puts forward the graded many-valued modal logic G(S5). Secondly, by employing the graded operators that correspond to graded modal operations in G(S5), we introduce the concept of graded upper and lower rough truth degrees of a logical formula. Then, we propose the graded upper and lower conditional rough truth degrees. Several basic interesting properties are addressed. Finally, in order to make a distinction between any two rough formulas in graded many-valued modal logic, the graded upper and lower rough similarity degrees between two graded modal formulas are established in a very natural way.