A formal deductive system for fuzzy propositional calculus

查看全文 作　　者：WANG [1]Guojun 机构地区：[1]Institute of Mathematics,Shaanxi Normal University,Xi’an 710062,China 出　　处：《Chinese Science Bulletin》索引1997年第42卷第18期,共5页 摘　　要：A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famous experts working in artificial intelligence and fuzzy systems refuted the opinion. Elkan then gave another report entitled 'The Paradoxical Controversy over Fuzzy Logic' as a reply to the refutations mentioned above. Prof. Wu gave a detailed analysis on the controversy (see ref. [3]). This shows that there is no rigid logic foundation for fuzzy propositional calculus. In this note we first point out that it is impossible to keep all classical theorems as tautologies in the field of fuzzy propositional calculus. Then we introduce a formal deductive system in fuzzy propositional calculus by giving up certain classical axioms, and the corresponding soundness theorem is proved. 关 键 词：∑R-tautology α-MP rule α-HS rule algebra of fuzzy formulas formal deductive system■(■) quotient algebra.