# Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning

arXiv: https://arxiv.org/abs/2201.09087 · HTML: https://mlsanity.com/paper/2201.09087/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2022.

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

- [Persistent Magnitude Homology for Quantitative Equational Theories](https://mlsanity.com/paper/2608.21479/) (2026)

## Abstract (arXiv)

The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend this framework in two orthogonal directions: algebras endowed with generalised metric space structures, and operations being nonexpansive up to a lifting. We apply our results to the algebraic axiomatisation of the Lukaszyk--Karmowski distance on probability distributions, which has recently found application in the field of representation learning on Markov processes.