Oppositions in a line segment

TL;DR

This paper introduces a novel approach to modeling oppositions within a one-dimensional line segment, contrasting with traditional two-dimensional frameworks based on the square of oppositions.

Contribution

It proposes a new construction for representing oppositions on a one-dimensional line segment, expanding the conceptual framework beyond classical two-dimensional models.

Findings

New one-dimensional opposition model

Contrasts with classical two-dimensional models

Potential applications in logical analysis

Abstract

Traditional oppositions are at least two-dimensional in the sense that they are built based on a famous bidimensional object called square of oppositions and on one of its extensions such as Blanch\'e's hexagon. Instead of two-dimensional objects, this article proposes a construction to deal with oppositions in a one-dimensional line segment.