Diagrams of opposition: an algebraic viewpoint

TL;DR

This paper explores the square of opposition and its geometric generalizations using algebraic structures, broadening the understanding of opposition diagrams beyond traditional logic.

Contribution

It introduces an algebraic framework to model various shapes of opposition and demonstrates its applicability to structures beyond classical logic.

Findings

Algebraic structures can represent different opposition diagrams.

The framework extends to non-traditional geometric generalizations.

Provides a unified algebraic perspective on opposition shapes.

Abstract

We study the square of opposition and its various geometric generalizations from an algebraic viewpoint. In particular, we show how the various shapes of oppositions can be framed under an algebraic framework and we illustrate this approach with algebraic structures beyond the traditional logical structures.