模糊模态逻辑系统M■uk中的可达广义重言式

Exact generalized tautologies in fuzzy modal logic system M■uk

将赋值格取为单位区间并将二元关系R模糊化,研究了模糊模态逻辑系统M■uk,然后将其赋值格离散化研究了多值模态逻辑系统M■n;证明了在M■n中,对任一可能的赋值α都存在可达α-重言式;在M■uk中对任一有理数α∈[0,1]都存在可达α-重言式;指出了在R0系统中起关键作用的升级算法对M■n系统已不再适用,并分析了其原因。

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