Lukasie wicz命题集的积分真度、发散度与相容度的分布

Distributions of the intergrated truth degrees,divergent degrees and consistency degrees in Lukasiewicz logic

研究了Lukasiewicz命题集的积分真度、发散度与相容度在[0,1]中的分布问题.利用一组公式所对应的McNaughtom函数,证明了Lukasiewicz逻辑系统中积分真度之集在[0,1]中稠密、发散度取值之集在[0,1]中稠密.结果表明,当Γ有限且相容时,相容度取值之集在[1/2,1]中稠密.

The distributions of the intergrated truth degrees, divergent degrees and consistency degrees in Lukasiewicz logic are discussed. Based on an analysis of the McNaughton founctions which are corresponded to a kind of formulas, it is proved that the set of all the intergrated truth degrees are dense in [0,1]. The density of divergent degrees in [ 0,1 ] is proved and the set of all the consistency degrees is proved to be dense in [ 1/2,1] when Г is finite and consistent.