Several characterizations of the 4--valued modal algebras

TL;DR

This paper explores various characterizations of 4-valued modal algebras, generalizing previous 3-valued Lukasiewicz algebras, and highlights their connections with other algebraic structures related to logic.

Contribution

It provides new characterizations of 4-valued modal algebras, emphasizing their relation to other well-known algebraic structures in logic.

Findings

Multiple characterizations of 4-valued modal algebras are presented.

The work demonstrates the algebraic closeness to other logical algebra structures.

Connections with known algebraic systems are established.

Abstract

A. Monteiro, in 1978, defined the algebras he named tetravalent modal algebras, will be called 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 [6,7,8,9,10,11,12] and by A. V. Figallo in [2,3,4,5]. J. Font and M. Rius indicated, in the introduction to the important work [1], 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.