Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2011, Article ID 268683, 3 pages doi:10.1155/2011/268683 Editorial BCK-Algebras and Related Algebraic Systems Young Bae Jun, 1 Ivan Chajda, 2 Hee Sik Kim, 3 Eun Hwan Roh, 4 Jianming Zhan, 5 and Afrodita Iorgulescu 6 1 Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Republic of Korea 2 Department of Algebra and Geometry, Faculty of Sciences, Palacky University (UP), 771 47 Olomouc, Czech Republic 3 Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea 4 Department of Mathematics Education, Chinju National University of Education, Chinju 660-756, Republic of Korea 5 Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei 445000, China 6 Department of Computer Science, The Bucharest Academy of Economic Studies, 010374 Bucharest, Romania Correspondence should be addressed to Young Bae Jun, skywine@gmail.com Received 5 November 2011; Accepted 10 November 2011 Copyright q 2011 Young Bae Jun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. BCK/BCI-algebras are algebraic structures, introduced by K. Is´ eki in 1966, that describe fragments of the propositional calculus involving implication known as BCK/BCI-logics. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. We refer the reader for useful textbooks for BCK/ BCI-algebra to 1–3. The aim of this special issue was to promote the exchange of ideas between researchers and to spread new trends in this area. It is focused on all aspects of BARAS, from their foundations to applications in computer sciences and informatics. This special issue contains nine papers. In the paper entitled “Commutative pseudo valuations on BCK-algebras,” M. I. Doh and M. S. Kang introduced the notion of a commu-tative pseudo valuation on a BCK-algebra and investigated its characterizations. They discussed the relationship between a pseudo valuation and a commutative pseudo valua-tion. They also provided conditions for a pseudo valuation to be a commutative pseudo valuation. Neggers et al. 4 introduced the notion of Q-algebras which are a generalization of BCK/ BCI/BCH-algebras, obtained several properties, and discussed quadratic Q-algebras. In the paper, entitled “A construction of mirror Q-algebras,” K. S. So introduced the notion of mirror algebras to Q-algebras, and she investigated how to construct mirror Q-algebras