Quantitative Algebraic Reasoning

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...

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Bibliographic Details
Published inProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 700 - 709
Main Authors Mardare, Radu, Panangaden, Prakash, Plotkin, Gordon
Format Conference Proceeding
LanguageEnglish
Published New York, NY, USA ACM 05.07.2016
SeriesACM Conferences
Subjects
Theory of computation
Theory of computation > Logic
Theory of computation > Models of computation
Theory of computation > Models of computation > Computability
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ISBN9781450343916
1450343910
DOI10.1145/2933575.2934518

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Summary: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 and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.
ISBN:9781450343916
1450343910
DOI:10.1145/2933575.2934518