Deductive Systems in Hyper EQ-Algebras
Received:March 08, 2016  Revised:December 23, 2016
Key Word: hyper EQ-algebra   (strong) deductive system   (positive) implicative strong deductive system   $S_{\rightarrow}$-reflexive subset   $S_{\otimes}$-semiclosed subset  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11571281), Independent Innovation Project of Graduate Students in Northwestern University (Grant No.YZZ15069) and Scientific Research Project of Xi'an Peihua University (Grant No.PHKT16075).
Author NameAffiliation
Xiaoyun CHENG School of Mathematics, Northwest University, Shaanxi 710127, P. R. China; General Education Center, Xi'an Peihua University, Shaanxi 710065, P. R. China 
Xiaolong XIN School of Mathematics, Northwest University, Shaanxi 710127, P. R. China 
Yongwei YANG School of Mathematics and Statistics, Anyang Normal University, Henan 455000 P. R. China 
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      In this paper, we introduce and investigate some types of deductive systems in hyper EQ-algebras and discuss relationships among them. Especially, we focus on investigating two types of important deductive systems, namely, (positive) implicative strong deductive systems, respectively. Moreover we give equivalent characterizations of them.
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