  In this paper we establish a new characterization of 4-valued modal algebras
considered by A. Monteiro. In order to obtain this characterization we
introduce a new class of algebras named generalized I-algebras. This class
contains strictly the class of C-algebras defined by Y. Komori as an algebraic
counterpart of the infinite-valued implicative Lukasiewicz propositional
calculus. On the other hand, the relationship between I-algebras and
conmutative BCK-algebras, defined by S. Tanaka in 1975, allows us to say that
in a certain sense G-algebras are also a generalization of these latter
algebras
