Quantitative Algebraic Reasoning

Radu Iulian Mardare; Prakash Panangaden; Gordon Plotkin

doi:10.1145/2933575.2934518

Quantitative Algebraic Reasoning

Radu Iulian Mardare, Prakash Panangaden, Gordon Plotkin

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

48 Citationer (Scopus)

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 and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.

Originalsprog	Engelsk
Titel	Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science : LICS'16, New York, NY, USA, July 5-8, 2016
Antal sider	10
Forlag	Association for Computing Machinery
Publikationsdato	2016
Sider	700-709
ISBN (Trykt)	978-1-4503-4391-6
DOI	https://doi.org/10.1145/2933575.2934518
Status	Udgivet - 2016
Begivenhed	31st IEEE Symposium on Logic in Computer Science - Columbia University, New York City, USA Varighed: 5 jul. 2016 → 8 jul. 2016 Konferencens nummer: 31st http://lics.rwth-aachen.de/lics16/

Konference

Konference	31st IEEE Symposium on Logic in Computer Science
Nummer	31st
Lokation	Columbia University
Land/Område	USA
By	New York City
Periode	05/07/2016 → 08/07/2016
Internetadresse	http://lics.rwth-aachen.de/lics16/

Adgang til dokumentet

10.1145/2933575.2934518

AUB Link

Søg efter materialet i Aalborg Universitetsbiblioteks søgemaskine

Approximate Reasoning for Stochastic Markovian Systems
Mardare, R. & Larsen, K. G.
01/11/2015 → 31/10/2019
Projekter: Projekt › Forskning

Citationsformater

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title = "Quantitative Algebraic Reasoning",

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 and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.",

author = "Mardare, {Radu Iulian} and Prakash Panangaden and Gordon Plotkin",

year = "2016",

doi = "10.1145/2933575.2934518",

language = "English",

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booktitle = "Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science",

publisher = "Association for Computing Machinery",

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note = "31st IEEE Symposium on Logic in Computer Science, LICS ; Conference date: 05-07-2016 Through 08-07-2016",

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Mardare, RI, Panangaden, P & Plotkin, G 2016, Quantitative Algebraic Reasoning. i Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science: LICS'16, New York, NY, USA, July 5-8, 2016. Association for Computing Machinery, s. 700-709, 31st IEEE Symposium on Logic in Computer Science, New York City, USA, 05/07/2016. https://doi.org/10.1145/2933575.2934518

Quantitative Algebraic Reasoning. / Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon.
Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science: LICS'16, New York, NY, USA, July 5-8, 2016. Association for Computing Machinery, 2016. s. 700-709.

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

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N2 - 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 and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.

AB - 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 and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.

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ER -

Quantitative Algebraic Reasoning

Abstract

Konference

Adgang til dokumentet

AUB Link

Fingeraftryk

Projekter

Approximate Reasoning for Stochastic Markovian Systems

Citationsformater