Reducing multiplicities in class diagrams

In class diagrams, so-called multiplicities are integer ranges attached to association ends. They constrain the number of instances of the associated class that an instance may be linked to, or in an alternative reading, the number of links to instances of the associated class. In complex diagrams with several chains of associations between two classes (arising e.g. in configuration management) it may happen that the lower or upper bound of a range can never be attained because of restrictions imposed by a parallel chain. In this paper we investigate how multiplicities behave when chaining associations together, and we characterise situations where intervals can be tightened due to information from other chains. Detecting and eliminating such redundancies provides valuable feedback to the user, as redundancies may hint at some underlying misconception.