SysMLv1: Some invalid multiplicity examples with navigable and non-navigable Association ends. In Cameo Systems Modeler with validation.

To make things a bit clearer, UML-style Classifier owner dot notation has been enabled under the Project Options for Magic Cyber-Systems Engineer^® (Cameo Systems Modeler^®). This optional dot notation from UML was dropped in "official" SysMLv1, but can still be activated in Cameo and can be a useful learning aid. It's best to always switch dot notation it off again after you've explored it, since it leads to diagram clutter.

The 1st case (top A-B) should be obvious. An instance of B can't be composed by two separate instances of A at once.

The 2nd case (middle A- C) is a bit trickier. It validates but you can in fact break it. You could use additional Object Constraint Language (OCL) rules in your model to catch the pathological instance arrangement.

The 3rd case (lower left A-D) produces a validation warning. The logic is that in this case if a D can't "know" about its owning A, so there's no point in having a named end 'a:A' when then Association is not navigable from D to A. Note that the tool can navigate it anyway for queries, even if it's non-navigable and the A end is not named.

Finally, the 4th case (lower right A-E) shows a valid case with the default SysMLv1 multiplicities for the diamond end explicitly provided:

SysML1.7: 'SysML defines defaults for multiplicities on the ends of specific types of associations. A part or shared association has a default multiplicity of [0..1] on the black or white diamond end. A unidirectional association has a default multiplicity of 1 on its target end.'

Visit also: SysMLv1: A part Property or reference Property is not necessarily a 'memberEnd' or 'ownedEnd' of an Association ('association' or 'owningAssociation'). But an Association always as at least 2 'memberEnd' Properties. [With some MagicDraw/Cameo tool tips.]

Some relevant quotes from the UML2.5.1 spec:

UML-2.5.1: 'Aggregation type, navigability, and end ownership are separate concepts, each with their own explicit notation. Association ends owned by classes are always navigable, while those owned by associations may be navigable or not.'

UML-2.5.1: 'Ownership of Association ends by an associated Classifier may be indicated graphically by a small filled circle, which for brevity we will term a dot. The dot is to be drawn integral to the graphic path of the line, at the point where it meets the Classifier, inserted between the end of the line and the side of the node representing the Classifier.'

UML-2.5.1: 'The dot shows that the model includes a Property of the type represented by the Classifier touched by the dot. This Property is owned by the Classifier at the other end.'

Note also that a Property may also exist alone without an Association. Visit also:

UML-2.5.1: 'A Property may represent an attribute of a Classifier, a memberEnd of an Association, or in some cases both simultaneously.'

SysMLv1: A part Property or reference Property is not necessarily a 'memberEnd' or 'ownedEnd' of an Association ('association' or 'owningAssociation'). But an Association always as at least 2 'memberEnd' Properties. [With some MagicDraw/Cameo tool tips.]

You can review your understanding of Associations with these two course slides:

Association and Property - some cases

Association and Property - some cases - with dot notation and ownership indicators

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