Betweenness algebras

TL;DR

This paper introduces betweenness algebras, a class of Boolean algebras with operators related to betweenness relations, providing a unifying framework for various betweenness structures in the literature.

Contribution

It defines and studies betweenness algebras with common axioms, connecting algebraic and relational perspectives, and introduces operators of possibility and sufficiency.

Findings

Established axioms for betweenness algebras

Connected algebraic structures to ternary frames

Developed operators of possibility and sufficiency

Abstract

We introduce and study a class of betweenness algebras-Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which makes our work applicable to a wide range of betweenness structures studied in the literature. On the algebraic side, we work with two operators of possibility and of suffciency.