Meaning, Choice and Algebraic Semantics of Similarity Based Rough Set Theory

TL;DR

This paper develops a comprehensive algebraic semantics for similarity-based rough set theory, incorporating choice operations and modal logic connections to handle all distinguishability concepts in similarity spaces.

Contribution

It introduces a novel algebraic semantics framework that addresses all forms of distinguishability in similarity spaces, extending prior approaches.

Findings

A new semantics based on local clear distinguishability is proposed.

Choice-related operations are integrated into the algebraic framework.

Connections with modal logics are established.

Abstract

Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the context. In this research, the essence of an algebraic semantics that can deal with all possible concepts of distinguishability over similarity spaces is progressed. Key to this is the addition of choice-related operations to the semantics that have connections with modal logics as well. Among these we focus on a semantics that is based on local clear distinguishability over similarity spaces.