British Journal of Mathematics & Computer Science 8(4): 274-285, 2015, Article no.BJMCS.2015.161 ISSN: 2231-0851 SCIENCEDOMAIN international www.sciencedomain.org _____________________________________ *Corresponding author: E-mail: hylinin@163.com; Filtrations and Deductive Systems in BCL + Algebras Yonghong Liu 1* 1 School of Automation, Wuhan University of Technology, Wuhan, 430070, P.R. China. Author’s contribution The only author performed the whole research work. Author YL wrote the first draft of the paper. Author YL read and approved the final manuscript. Article Information DOI: 10.9734/BJMCS/2015/15901 Editor(s): (1) Dijana Mosic, Department of Mathematics, University of Niˇs, Serbia. (2) Radko Mesiar, Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology Bratislava, Slovakia. (3) Vyacheslav Pivovarchik, Dept. of Applied Mathematics and Computer Science, South-Ukrainian National Pedagogical University, Ukraine. (4) Tian-Xiao He,Department of Mathematics and Computer Science, Illinois Wesleyan University, USA. Reviewers: (1) Anonymous, India. (2) Anonymous, Turkey. (3) Anonymous, USA. (4) Anonymous, China. (5) Anonymous, Korea. Complete Peer review History: http://www.sciencedomain.org/review-history.php?iid=1033&id=6&aid=8699 Received: 24 December 2014 Accepted: 10 March 2015 Published: 06 April 2015 _______________________________________________________________________ Abstract The aim of this paper is to introduce the two notions of filtrations and deductive systems in BCL + algebras, and investigate some of their related properties. Using this, we prove that the filtration is subalgebra of BCL + algebras; we also prove that the filtration of BCL + algebras is a deductive system to the filtration of BCL + algebras with certain relations. Keywords: BCL algebras; BCL + algebras; filtrations; deductive systems. 2010 Mathematics Subject Classification: 03G25, 06F99. 1 Introduction The present author (2011 and 2012) [1,2] first introduced of BCL-algebras and BCL + -algebras. Later on, more papers have appeared in which BCL algebras and their related concepts were Original Research Article