On Generalized I-Algebras and 4-valued Modal Algebras

TL;DR

This paper introduces generalized I-algebras to characterize 4-valued modal algebras, linking them to C-algebras and BCK-algebras, thereby expanding the algebraic framework for many-valued modal logic.

Contribution

It defines generalized I-algebras, providing a new characterization of 4-valued modal algebras and connecting them to existing algebraic structures like C-algebras and BCK-algebras.

Findings

Generalized I-algebras characterize 4-valued modal algebras.

G-algebras encompass C-algebras and are related to BCK-algebras.

New algebraic relationships enhance understanding of many-valued modal logic.

Abstract

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