Quantitative Algebraic Reasoning

Radu Mardare, Prakash Panangaden, Gordon Plotkin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative equational theory whose free algebras correspond to well known structures. In each case we have finitary and continuous versions. The four cases are: Hausdorff metrics from quantitive semilattices; p-Wasserstein metrics (hence also the Kantorovich metric) from barycentric algebras andalso from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.
Original languageEnglish
Title of host publicationLICS '16 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
Place of PublicationNew York, USA
PublisherACM
Pages700-709
Number of pages10
ISBN (Print)978-1-4503-4391-6
DOIs
Publication statusPublished - 5 Jul 2016
Event31st Annual ACM/IEEE Symposium on Logic in Computer Science - New York City, United States
Duration: 5 Jul 20168 Jul 2016
http://lics.siglog.org/lics16/

Conference

Conference31st Annual ACM/IEEE Symposium on Logic in Computer Science
Abbreviated titleLICS 2016
CountryUnited States
CityNew York City
Period5/07/168/07/16
Internet address

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