DeepAI
Log In Sign Up

Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning

01/22/2022
by   Matteo Mio, et al.
0

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 Łukaszyk–Karmowski distance on probability distributions, which has recently found application in the field of representation learning on Markov processes.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/20/2018

Free complete Wasserstein algebras

We present an algebraic account of the Wasserstein distances W_p on comp...
05/15/2020

Monads and Quantitative Equational Theories for Nondeterminism and Probability

The monad of convex sets of probability distributions is a well-known to...
04/28/2022

On Quantitative Algebraic Higher-Order Theories

We explore the possibility of extending Mardare et al. quantitative alge...
08/06/2011

Algebraic Geometric Comparison of Probability Distributions

We propose a novel algebraic framework for treating probability distribu...
01/25/2022

Structured Handling of Scoped Effects: Extended Version

Algebraic effects offer a versatile framework that covers a wide variety...
05/31/2019

The cut metric for probability distributions

Guided by the theory of graph limits, we investigate a variant of the cu...