Distributions of truth degrees, divergent degrees and consistency degrees in the logic system n
YU Hai1,2, ZHAN Wan-rong1,2, WANG Guo-jun1*
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China; 2 College of Mathematics and Science, Luoyang Normal College, Luoyang 471022, Henan, China)
Abstract:
The distributions of truth degrees, divergent degrees and consistency degrees in the n-valued ukasiewicz propositional logic system n are discussed. Letting H={k/nm｜k=0,…,nm;m=1,2,…}, it is proved by means of McNaughton function that there exists a formula A with the truth degree k/nm. Thus, the set of all truth degrees of formulas is dense in ［0,1］. It is also proved that the set of all divergent degrees of theories is the unit interval ［0,1］ by the density of truth degrees of formulas and generalized deduction theorem of system n. According to the relation between consistency degrees and divergent degrees, it is induced that the set of all consistency degrees of theories is {0}∪ ［1/2,1］.
KeyWords:
logic system n; truth degree; divergent degree; consistency degree
