Modal R0-Algebra-Valued Modal Logic System ML ∗

Based on the concept of the R0-algebra, the present paper intro- duces the definition of the modal R0-algebra by adding a new unary operator , corresponding to modalities of the modal logic. By use of modal R0- algebras, semantic and syntactic frameworks are constructed, respectively, for logic system ML ∗ , the modal R0-algebra-valued modal logic system. It is pointed out that the semantics of system ML ∗ generalizes the semantics of both the classical modal logic and the (0, 1)-valued modal logic. The main result of the paper is the completeness theorem of system ML ∗ .