# Frank's triangular norms in Piaget's logical proportions

arXiv: https://arxiv.org/abs/2408.03795 · HTML: https://mlsanity.com/paper/2408.03795/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 11 references that are in the map.
- First posted on arXiv 7 Aug 2024.

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

- [From numerical proportions to analogical proportions between probabilities](https://mlsanity.com/paper/2606.23029/) (2026)

## Abstract (arXiv)

Starting from the Boolean notion of logical proportion in Piaget's sense, which turns out to be equivalent to analogical proportion, this note proposes a definition of analogical proportion between numerical values based on triangular norms (and dual co-norms). Frank's family of triangular norms is particularly interesting from this perspective. The article concludes with a comparative discussion with another very recent proposal for defining analogical proportions between numerical values based on the family of generalized means.