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 representation of Stone relation algebras and for Stone relation algebras to be relation algebras.

翻译：先前的工作对关系代数中的基数运算进行了公理化，该运算用于计算无权重图的边数。我们将基数公理推广到Stone关系代数（该类代数建模加权图），并研究了基数各公理之间的关系。由此，我们也为关系代数得到了更简洁的基数公理。本文给出了Stone关系代数可表示性的充分条件，以及Stone关系代数为关系代数的充分条件。