Schematic Extensions of MTL by Adding Weak Divisibility Axiom  

作　　者：ZHOU Jianren WU Hongbo 

机构地区：[1]School of Mathematics and Information Sciences, Shaanxi Normal University

出　　处：《Chinese Journal of Electronics》2016年第5期824-831,共8页电子学报（英文版）

基　　金：supported by National Natural Science Foundation of China(No.61572016,No.11531009);the Fundamental Research Funds for the Central Universities(No.GK201501001)

摘　　要：MTL is a Monoidal t-norm based logic introduced by Esteva and Godo by omitting divisibility axiom from H′ajek's Basic logic(BL). Many logics can be obtained by adding axioms to MTL logic. Logic system WBL is obtained by adding weak divisibility axiom to logic system MTL. Logic system WMV is obtained by adding involution axiom to logic system WBL. WBL-algebra corresponding to logic system WBL and WMV-algebra to logic system WMV are defined respectively. It is proved that the both of logic system Luk and logic system Nilpotent minimum(NM) are the schematic extensions of logic system WMV. Weak Wajsberg algebra and the simplified form of logic system WMV are obtained.MTL is a Monoidal t-norm based logic introduced by Esteva and Godo by omitting divisibility axiom from H′ajek＇s Basic logic（BL）. Many logics can be obtained by adding axioms to MTL logic. Logic system WBL is obtained by adding weak divisibility axiom to logic system MTL. Logic system WMV is obtained by adding involution axiom to logic system WBL. WBL-algebra corresponding to logic system WBL and WMV-algebra to logic system WMV are defined respectively. It is proved that the both of logic system Luk and logic system Nilpotent minimum（NM） are the schematic extensions of logic system WMV. Weak Wajsberg algebra and the simplified form of logic system WMV are obtained.

关 键 词：Many-valued logic Monoidal t-norm based logic（MTL） WBL logic WMV logic Weak Wajsberg algebra Simplification 

分 类 号：O141[理学—数学]