On the semilattice of modal operators and decompositions of the discriminator

TL;DR

This paper explores the structure of modal operators on Boolean algebras, focusing on their join semilattice and the decomposition of the discriminator through pairs of modal operators, contributing to the algebraic understanding of modal logic.

Contribution

It introduces a detailed analysis of the join semilattice of modal operators and characterizes pairs that decompose the discriminator on Boolean algebras.

Findings

Characterization of the join semilattice of modal operators.

Identification of pairs of modal operators whose supremum is the discriminator.

Insights into bi-modal algebras related to these operators.

Abstract

We investigate the join semilattice of modal operators on a Boolean algebra $B$. Furthermore, we consider pairs $(f,g)$ of modal operators whose supremum is the unary discriminator on $B$, and study the associated bi--modal algebras.