Quantitative research of generalized tautologies in n-valued propositional logic Ｌｎ
WANG Guo-jun1,2, SHI Hui-xian1
(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:
By means of the infinite product of evenly distributed probability spaces, the proportion of the class of valuation which satisfies v(A)≥ζ (or v(A)＞ζ, where ζ∈［0,1］) in the set of all valuations is considered and the concepts of ζ-truth degree and ζ＋-truth degree in ｎ-valued Ｒ０-propositional logic system Ｌｎ are introduced in order to double-grade the concept of tautology. Also, the theories of σ-(ζ-tautology) and σ-(ζ＋-tautology) are defined. Moreover, relationships between ζ-truth degree (ζ＋-truth degree) and generalized tautology together with the graded generalized tautology are discussed and the general reference rules endowed with ζ-truth degree are proved.
KeyWords:
generalized tautology; ζ-truth degree; σ-(ζ-tautology); general reference rule
