Analogical proportions in monounary algebras

TL;DR

This paper investigates how analogical proportions can be characterized within monounary algebras, specifically using the natural numbers and the successor function, revealing a relation based on difference proportions.

Contribution

It introduces a characterization of analogical proportions in monounary algebras, focusing on the infinite case with natural numbers and the successor function.

Findings

Analogical proportions are characterized by difference proportions in the natural numbers.

The study provides a formal relation for analogies in monounary algebras.

The approach applies to infinite monounary algebras with a unary function.

Abstract

This paper studies analogical proportions in monounary algebras consisting only of a universe and a single unary function. We show that the analogical proportion relation is characterized in the infinite monounary algebra formed by the natural numbers together with the successor function via difference proportions.