# Bilingual analogical proportions via hedges

arXiv: https://arxiv.org/abs/2305.05614 · HTML: https://mlsanity.com/paper/2305.05614/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 2 May 2023.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 1 of 1)

- [Anti-unification and Generalization: A Survey](https://mlsanity.com/paper/2302.00277/) (2023)

## Abstract (arXiv)

Analogical proportions are expressions of the form ``a is to b what c is to d'' at the core of analogical reasoning which itself is at the core of human and artificial intelligence. The author has recently introduced em from first principles an abstract algebro-logical framework of analogical proportions within the general setting of universal algebra and first-order logic. In that framework, the source and target algebras have the em same underlying language. The purpose of this paper is to generalize his unilingual framework to a bilingual one where the underlying languages may differ. This is achieved by using hedges in justifications of proportions. The outcome is a major generalization vastly extending the applicability of the underlying framework. In a broader sense, this paper is a further step towards a mathematical theory of analogical reasoning.