BCI-Algebra-(BCI-Algebra)

Author: None
Publisher:
Publish Date: 2006-12-01
Features: This book is mainly designed for the graduate students who are interested in the theory of BCI and BCK-algebras. BCI-algebras are a wider class than BCK-algebras, introduced by Kiyoshi Iseki in 1966. BCI-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the implicational functor in logical systems. They are closely related to partially ordered commutative monoids as well as various logical algebras. Their names are originated from the combinators b, c, k and i in combinatory logic. The early research work was mainly carried out among the Japanese mathematicians Kiyoshi Iseki and Shota Tanaka, etc., who did a great deal of foundation work. Since the late 1970s, their work has been paid much attention. In particular, the participation in the research of Polish mathematicians Tadeusz Traczyk and Andrzej Wronski, as well as Australian mathematician William H. Cornish, etc., is making this branch of algebra develop rapidly. Many interesting and important results are discovered continuously. Now, the theory of BCI-algebras has been widely spread.