A Program in Dialectical Rough Set Theory

TL;DR

This paper explores extending dialectical rough set theory to more general frameworks, aiming to improve semantic clarity and formalize complex concepts in rough set analysis.

Contribution

It formulates a program for extending dialectical rough set theory to broader contexts, enhancing semantic understanding and formalization capabilities.

Findings

Provides minimal conditions for extending rough set semantics

Demonstrates improved semantics in complex cases

Outlines a program for future development of dialectical RST

Abstract

A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions on the nature of granularity, underlying semantic domain and nature of the general rough set theories (RST) involved for possible extension of the semantics to more general RST on a paradigm. On this basis we also formulate a program in dialectical rough set theory. The dialectical approach provides better semantics in many difficult cases and helps in formalising a wide variety of concepts and notions that remain untamed at meta levels in the usual approaches. This is a brief version of a more detailed forthcoming paper by the present author.