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; pWasserstein 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 language  English 

Title of host publication  LICS '16 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science 
Place of Publication  New York, USA 
Publisher  ACM 
Pages  700709 
Number of pages  10 
ISBN (Print)  9781450343916 
DOIs  
Publication status  Published  5 Jul 2016 
Event  31st Annual ACM/IEEE Symposium on Logic in Computer Science  New York City, United States Duration: 5 Jul 2016 → 8 Jul 2016 http://lics.siglog.org/lics16/ 
Conference
Conference  31st Annual ACM/IEEE Symposium on Logic in Computer Science 

Abbreviated title  LICS 2016 
Country  United States 
City  New York City 
Period  5/07/16 → 8/07/16 
Internet address 
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Profiles

Gordon Plotkin
 School of Informatics  Professor
 Laboratory for Foundations of Computer Science
 Foundations of Computation
Person: Academic: Research Active