WANG Guo-jun1,2, GAO Xiang-ni1
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China; 2 Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China)
Abstract:
The concept of truth degree of a logic theory is proposed firstly in the present paper, which generalizes the truth degree of a formula to that of a set of formulas. The concept of divergence degree can be simplified thereby. Moreover, the relation η(Γ)=(1+τ(Γ))/2 between truth degree and consistency degree of a given logic theory Γ is obtained when Γ is consistent. Finally, in the propositional logic system C2, theories Γ1 and Γ2 are divided into six categories, in which the relation of truth degrees of logic theories Γ1, Γ2 and Γ1∪Γ2 are compared, respectively.
KeyWords:
truth degree of a logic theory; consistency degree; divergence degree; finite; countable
