Abstract:

The fuzzy modal logic system M?uk is introduced, where the evaluation lattice is taken to be the unite interval and the binary relation R is fuzzif ied, then it is discretized to be the multi-valued fuzzy modal logic system M? n. It is proved that for any possible value α in M?n there exists an exact  α-tautology; and in M?uk, for any rational α∈［0,1］, there exists  an exac t α-tautology. It is pointed out that the lift-algorithm which plays a key role in R₀ systems is not suitable for the system M?n, and the reasons are  analyzed.