On the Axiomatizability of Quantitative Algebras

Gordon Plotkin; Radu Mardare; Prakash Panangaden

doi:10.1109/LICS.2017.8005102

On the Axiomatizability of Quantitative Algebras

Gordon Plotkin, Radu Mardare, Prakash Panangaden

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by us in 2016. They provide the mathematical foundation for metric semantics of probabilistic, stochastic and other quantitative systems. This paper considers the issue of axiomatizability of
QAs. We investigate the entire spectrum of types of quantitative equations that can be used to axiomatize theories: (i) simple quantitative equations; (ii) Horn clauses with no more than c equations between variables as hypotheses, where c is a cardinal and (iii) the most general case of Horn clauses. In each case we characterize the class of QAs and prove variety/quasivariety theorems that extend and generalize classical results from model theory for algebras and first-order structures.

Original language	English
Title of host publication	2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Publisher	Institute of Electrical and Electronics Engineers
Number of pages	12
ISBN (Electronic)	978-1-5090-3018-7
DOIs	https://doi.org/10.1109/LICS.2017.8005102
Publication status	Published - 18 Aug 2017
Event	2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science - Reykjavik, Reykjavik, Iceland Duration: 20 Jun 2017 → 23 Jun 2017 http://lics.siglog.org/lics17/

Conference

Conference	2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science
Abbreviated title	LICS 2017
Country/Territory	Iceland
City	Reykjavik
Period	20/06/17 → 23/06/17
Internet address	http://lics.siglog.org/lics17/

Access to Document

10.1109/LICS.2017.8005102

Varieties-LICS-1Accepted author manuscript, 322 KB

http://ieeexplore.ieee.org/abstract/document/8005102/

Cite this

@inproceedings{655773acadab42e29f5c0ab13e4bdf9e,

title = "On the Axiomatizability of Quantitative Algebras",

abstract = "Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by us in 2016. They provide the mathematical foundation for metric semantics of probabilistic, stochastic and other quantitative systems. This paper considers the issue of axiomatizability ofQAs. We investigate the entire spectrum of types of quantitative equations that can be used to axiomatize theories: (i) simple quantitative equations; (ii) Horn clauses with no more than c equations between variables as hypotheses, where c is a cardinal and (iii) the most general case of Horn clauses. In each case we characterize the class of QAs and prove variety/quasivariety theorems that extend and generalize classical results from model theory for algebras and first-order structures.",

author = "Gordon Plotkin and Radu Mardare and Prakash Panangaden",

year = "2017",

month = aug,

day = "18",

doi = "10.1109/LICS.2017.8005102",

language = "English",

booktitle = "2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 ; Conference date: 20-06-2017 Through 23-06-2017",

url = "http://lics.siglog.org/lics17/",

}

TY - GEN

T1 - On the Axiomatizability of Quantitative Algebras

AU - Plotkin, Gordon

AU - Mardare, Radu

AU - Panangaden, Prakash

PY - 2017/8/18

Y1 - 2017/8/18

N2 - Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by us in 2016. They provide the mathematical foundation for metric semantics of probabilistic, stochastic and other quantitative systems. This paper considers the issue of axiomatizability ofQAs. We investigate the entire spectrum of types of quantitative equations that can be used to axiomatize theories: (i) simple quantitative equations; (ii) Horn clauses with no more than c equations between variables as hypotheses, where c is a cardinal and (iii) the most general case of Horn clauses. In each case we characterize the class of QAs and prove variety/quasivariety theorems that extend and generalize classical results from model theory for algebras and first-order structures.

AB - Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by us in 2016. They provide the mathematical foundation for metric semantics of probabilistic, stochastic and other quantitative systems. This paper considers the issue of axiomatizability ofQAs. We investigate the entire spectrum of types of quantitative equations that can be used to axiomatize theories: (i) simple quantitative equations; (ii) Horn clauses with no more than c equations between variables as hypotheses, where c is a cardinal and (iii) the most general case of Horn clauses. In each case we characterize the class of QAs and prove variety/quasivariety theorems that extend and generalize classical results from model theory for algebras and first-order structures.

U2 - 10.1109/LICS.2017.8005102

DO - 10.1109/LICS.2017.8005102

M3 - Conference contribution

BT - 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

PB - Institute of Electrical and Electronics Engineers

T2 - 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science

Y2 - 20 June 2017 through 23 June 2017

ER -

On the Axiomatizability of Quantitative Algebras

Abstract

Conference

Access to Document

Fingerprint

Cite this