# Analogical proportions in monounary algebras

arXiv: https://arxiv.org/abs/2208.06829 · HTML: https://mlsanity.com/paper/2208.06829/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 35 references that are in the map.
- First posted on arXiv 14 Aug 2022.

## Builds on (most cited first, 4 of 4)

- [Analogical Dissimilarity: Definition, Algorithms and Two Experiments in Machine Learning](https://mlsanity.com/paper/1401.3427/) (2014)
- [Analogical proportions](https://mlsanity.com/paper/2006.02854/) (2020)
- [Logic program proportions](https://mlsanity.com/paper/1809.09938/) (2018)
- [Inapproximability of Unique Games in Fixed-Point Logic with Counting](https://mlsanity.com/paper/2104.04566/) (2021)

## Built on by (most cited first, 2 of 2)

- [Proportoids](https://mlsanity.com/paper/2210.01751/) (2022)
- [Algebraic anti-unification](https://mlsanity.com/paper/2407.15510/) (2024)

## Abstract (arXiv)

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.