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

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

48 Citations (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.

Original language	English
Title of host publication	Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science : LICS'16, New York, NY, USA, July 5-8, 2016
Number of pages	10
Publisher	Association for Computing Machinery
Publication date	2016
Pages	700-709
ISBN (Print)	978-1-4503-4391-6
DOIs	https://doi.org/10.1145/2933575.2934518
Publication status	Published - 2016
Event	31st IEEE Symposium on Logic in Computer Science - Columbia University, New York City, United States Duration: 5 Jul 2016 → 8 Jul 2016 Conference number: 31st http://lics.rwth-aachen.de/lics16/

Conference

Conference	31st IEEE Symposium on Logic in Computer Science
Number	31st
Location	Columbia University
Country/Territory	United States
City	New York City
Period	05/07/2016 → 08/07/2016
Internet address	http://lics.rwth-aachen.de/lics16/

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10.1145/2933575.2934518

AUB Link

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Approximate Reasoning for Stochastic Markovian Systems
Mardare, R. & Larsen, K. G.
01/11/2015 → 31/10/2019
Project: Research

Cite this

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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",

address = "United States",

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. in 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, pp. 700-709, 31st IEEE Symposium on Logic in Computer Science, New York City, United States, 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. p. 700-709.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

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T1 - Quantitative Algebraic Reasoning

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AU - Panangaden, Prakash

AU - Plotkin, Gordon

N1 - Conference code: 31st

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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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DO - 10.1145/2933575.2934518

M3 - Article in proceeding

SN - 978-1-4503-4391-6

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T2 - 31st IEEE Symposium on Logic in Computer Science

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ER -

Quantitative Algebraic Reasoning

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Approximate Reasoning for Stochastic Markovian Systems

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