On the axiomatizability of quantitative algebras

Radu Mardare, Prakash Panangaden, Gordon Plotkin

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

5 Citations (Scopus)

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 languageEnglish
Title of host publication32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
Place of PublicationPiscataway, N.J.
PublisherIEEE
Pages1-12
Number of pages12
ISBN (Electronic)9781509030187
DOIs
Publication statusPublished - 8 Aug 2017
Event32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 - Reykjavik, Iceland
Duration: 20 Jun 201723 Jun 2017

Conference

Conference32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
CountryIceland
CityReykjavik
Period20/06/1723/06/17

Keywords

  • algebra
  • mathematical model
  • extraterrestrial measurements
  • semantics
  • cognition

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