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arXiv · 2201.09087

Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning

Matteo Mio·Ralph Sarkis·Valeria Vignudelli
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Abstract

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 {\L}ukaszyk--Karmowski distance on probability distributions, which has recently found application in the field of representation learning on Markov processes.

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Matteo Mio, Ralph Sarkis, Valeria Vignudelli. 2022-01-22. Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning. https://arxiv.org/abs/2201.09087

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