A. Monteiro, in 1978, defined the algebras he named tetravalent modal algebras,? that will be called? {em $4-$valued modal algebras} in this work. These algebras constitute a generalization of the $3-$valued Lukasiewicz algebras defined by Moisil. The theory of the $4-$valued modal algebras has been widely developed by I. Loureiro in cite{IL1, IL2, IL3, IL4, IL5, IL6, IL7} and by A. V. Figallo in cite{FI3, FI4, AF.PL,AF.AZ}. J. Font and M. Rius indicated, in the introduction to the important work cite{JF.MR2}, a brief but detailed review on the $4-$valued modal algebras. In this work varied characterizations are presented that show the ``closeness'' this variety of algebras has with other well--known algebras related to the algebraic counterparts of certain logics.
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机译：1978年，A。Monteiro定义了代数，他将其称为四价模态代数。那将被称为？ { em $ 4- $值模态代数}。这些代数构成了Moisil定义的$ 3- $值的Lukasiewicz代数的推广。 I. Loureiro在 cite {IL1，IL2，IL3，IL4，IL5，IL6，IL7}中和由AV Figallo在 cite {FI3，FI4，AF中}广泛开发了$ 4- $模态代数的理论。 PL，AF.AZ}。 J. Font和M. Rius在重要著作 cite {JF.MR2}的导言中指出，对价值4美元的模态代数进行了简短而详尽的评论。在这项工作中，呈现了各种特征，这些特征显示了这种代数与其他与某些逻辑的代数对应物有关的众所周知的代数之间的``接近性''。
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