Theory of truth degrees of formulas in Lukasiewicz n-valued propositional logic and a limit theorem

作     者：LI Bijing WANG Guojun 

作者机构：Institute of Mathematics Shaanxi Normal University Xi'an 710062 China Research Center for Science Xi'an Jiaotong University Xi'an 710049 China 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2005年第48卷第6期

页      面：727-736页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10331010) 

主　　题：Lukasiewicz n-valued propositional logic truth degree limit theorem integrated truth degree 

摘      要：The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integrated truth function τ when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.