Discrete dualities for some algebras from rough sets

TL;DR

This paper explores discrete dualities linking classes of algebras derived from rough sets with relational systems, providing foundational representation theorems based on classical duality theories.

Contribution

It recalls and extends discrete dualities for algebras from rough sets, building on foundational work by Jönsson, Tarski, Kripke, and van Benthem.

Findings

Establishes duality theorems for rough set algebras

Provides representation results for these algebras

Connects algebraic and relational frameworks in rough set theory

Abstract

A discrete duality is a relationship between classes of algebras and classes of relational systems (frames) resulting in two representation theorems building on the early work of J\'onsson and Tarski, Kripke, and van Benthem. In this section we recall discrete dualities for various types of algebras arising from rough sets.