On Generalized I-Algebras and 4-valued Modal Algebras

摘要

In this paper we establish a new characterization of 4-valued modal algebrasconsidered by A. Monteiro. In order to obtain this characterization weintroduce a new class of algebras named generalized I-algebras. This classcontains strictly the class of C-algebras defined by Y. Komori as an algebraiccounterpart of the infinite-valued implicative Lukasiewicz propositionalcalculus. On the other hand, the relationship between I-algebras andconmutative BCK-algebras, defined by S. Tanaka in 1975, allows us to say thatin a certain sense G-algebras are also a generalization of these latteralgebras