Bilingual analogical proportions via hedges
On the map: LLM reasoning → Reasoning benchmarks and evaluation
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.
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.
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References · 1
- 2023Anti-unification and Generalization: A Surveycited by 7
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