On the axiomatizability of quantitative algebras

Radu Iulian Mardare, Prakash Panagaden, Gordon Plotkin

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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.
Titel2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
Publikationsdato8 aug. 2017
ISBN (Elektronisk)9781509030187
StatusUdgivet - 8 aug. 2017
Begivenhed32nd Annual ACM/IEEE Symposium on Logic in Computer Science ) - Reykjavik, Finland
Varighed: 20 jun. 201723 jun. 2017


Konference32nd Annual ACM/IEEE Symposium on Logic in Computer Science )

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