# Generalization-baed similarity

arXiv: https://arxiv.org/abs/2302.10096 · HTML: https://mlsanity.com/paper/2302.10096/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 70 references that are in the map.
- First posted on arXiv 13 Feb 2023.

## Builds on (most cited first, 7 of 7)

- [What Does Explainable AI Really Mean? A New Conceptualization of Perspectives](https://mlsanity.com/paper/1710.00794/) (2017)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Analogical proportions](https://mlsanity.com/paper/2006.02854/) (2020)
- [Logic program proportions](https://mlsanity.com/paper/1809.09938/) (2018)
- [Anti-unification and Generalization: A Survey](https://mlsanity.com/paper/2302.00277/) (2023)
- [Sequential composition of propositional logic programs](https://mlsanity.com/paper/2009.05774/) (2020)
- [Sequential composition of answer set programs](https://mlsanity.com/paper/2104.12156/) (2021)

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

- [Logic-based similarity](https://mlsanity.com/paper/2305.00065/) (2023)
- [Algebraic anti-unification](https://mlsanity.com/paper/2407.15510/) (2024)

## Abstract (arXiv)

Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops textitfrom the ground up an abstract algebraic and qualitative notion of similarity based on the observation that sets of generalizations encode important properties of elements. We show that similarity defined in this way has appealing mathematical properties. As we construct our notion of similarity from first principles using only elementary concepts of universal algebra, to convince the reader of its plausibility, we show that it can model fundamental relations occurring in mathematics and be naturally embedded into first-order logic via model-theoretic types. Finally, we sketch some potential applications to theoretical computer science and artificial intelligence.