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.

翻译：已有工作将关系代数中的基数运算公理化，该运算用于计算无权图的边数。我们将基数公理推广至刻画加权图的斯通关系代数，并研究基数各公理间的联系，由此也简化了关系代数的基数公理。我们给出了斯通关系代数的可表示性以及斯通关系代数成为关系代数的充分条件。