# Analogical proportions II

arXiv: https://arxiv.org/abs/2405.13461 · HTML: https://mlsanity.com/paper/2405.13461/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 45 references that are in the map.
- First posted on arXiv 22 May 2024.

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

- [Analogical proportions](https://mlsanity.com/paper/2006.02854/) (2020)
- [Logic program proportions](https://mlsanity.com/paper/1809.09938/) (2018)
- [Galois theory for analogical classifiers](https://mlsanity.com/paper/2205.04593/) (2022)
- [Proportoids](https://mlsanity.com/paper/2210.01751/) (2022)

## Built on by (most cited first, 1 of 1)

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

## Abstract (arXiv)

Analogical reasoning is the ability to detect parallels between two seemingly distant objects or situations, a fundamental human capacity used for example in commonsense reasoning, learning, and creativity which is believed by many researchers to be at the core of human and artificial general intelligence. Analogical proportions are expressions of the form ``a is to b what c is to d'' at the core of analogical reasoning. The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. It is the purpose of this paper to further develop the mathematical theory of analogical proportions within that framework as motivated by the fact that it has already been successfully applied to logic program synthesis in artificial intelligence.