Cardinality and Representation of Stone Relation Algebras

TL;DR

This paper extends the axioms for counting edges from unweighted to weighted graphs within Stone relation algebras, simplifying the axioms and exploring conditions for their representability and relation algebra properties.

Contribution

It generalizes the cardinality axioms to Stone relation algebras and provides conditions for their representability and relation algebra status.

Findings

Simplified cardinality axioms for Stone relation algebras

Conditions for Stone relation algebras to be relation algebras

Sufficient conditions for representability of Stone relation algebras

Abstract

Previous work has axiomatised the cardinality operation in relation algebras, which counts the number of edges of an unweighted graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study the relationships between various axioms for cardinality. This results in simpler cardinality axioms also for relation algebras. We give sufficient conditions for the representability of Stone relation algebras and for Stone relation algebras to be relation algebras.