MetaEdit+ features the "model explosion" link. So, one model contain contain an element that is "exploded" to a whole model. You find this also in the Yourdan Modern Strcutured Analysis book: a control process in a DFD is expanded into a state-transition diagram, which is a model on its own right. I would say that "explosion"/"expansion" is a special case of link type T1 (reference).

Undependently on the kind of platform used, it might be useful to specify "correspondences" between models with so-called weaving models, ie models defining many-to-many relations among the model elements. Alternatively, if besides the correspondences one would like to use them for establishing some model consistency management (ie a change in a model m1 will trigger changes in the other models), it might be interesting to give the correspondences in terms of "relations" in a bidirectional language like QVT-R or JTL.

For instance you might want to look at: Romina Eramo, Alfonso Pierantonio, José Raúl Romero, Antonio Vallecillo: Change Management in Multi-Viewpoint System Using ASP. EDOCW 2008: 433-440

Yes, the "model explosion" type is quite frequent. See also the decomposition of processes in data-flow diagrams (1970-ties).  The hint on horizontal vs. vertical is a useful one.

If a model is generated from another one by automatic model transformation, then the relation can be automatically added by the transformation tool. I think, this is a kind of an "implementation" link (T2).

To me, intra-model and inter-model consistency are conceptually the same. Just merge the models into one "super-model" and all constraints become intra-model...

Hi Domenik, the integration is of course a difficult task when two models are being developed independently from each other. There are integrated modeling tools that do provide different modeling languages and that do integrate them. My answer was referring to this scenario, not the more ambitious case where two independent modeling languages shall be integrated.

In the latter case, there could be large semantic overlaps and disparities which makes the integration task a real challenge and sometimes impossible.

In the first case, a method engineer has carefully crafted a set of interrelated modeling languages. A fine example are the modeling languages of "Modern Structured Analysis" (E. Yourdan). Yourdan specifically addresses the links in his chapter on balancing.

The ArchiMate notation has a list of link types that can cross boundaries between levels (and likewise between the Zachmanian modeling perspectives):

"realization": this roughly correspond to the "implementation" link (T2)

"used by": this appears to be  a mixture between T2 and the model explosion; for example an application service is used by a business function

There may be more link types that cross layers in ArchiMate but these appear to be the most frequent ones. As Archimate has no classical modeling language boundary, the inter-notational links between the Zachmanian dimensions follow from assigning the constructs to the respective Zachman dimension.

In MetaEdit+ we have in addition to ’model explosion’ also other linking possibilites, like ’decomposition’, ’property value sharing’, ’non-property sharing’, all being terms used in the tool. MetaEdit+, however, is a metamodeling tool, so users define their own languages and links, and sometimes the linking like ’explosion’ may be from an model object, or from a relationship between a set of objects, or form the connection end of the relationship.

While I would say that these cover a good set of most typically used ’inter-notational links’, there is at least 128 linking ways. Why 128? For my PhD work I made inductive analysis of modeling langauges and their metamodels to understand what kind of links they are using. The research approach was simple: identify different characterstics of linking as described in detail in Section 4.4.2 and in particular Table 4-4 (http://users.jyu.fi/~jpt/doc/thesis/ime-4_4.html). All combinations naturally do not exist (or at least I did not found those used in the modeling langauges analysed, and the evaluation should not be perhaps so simple as (yes/no) and I used. It would be interesting to examine a larger set of languages, and newer languages that are more complex in terms of their metamodels, like SysML, Autosar, East-ADL, AADL etc.

Thanks a lot Juha-Pekka! I agree that inter-notational links can hardly be distinguished from intra-notational ones. Modeling language designers pragmatically declare which constructs are part of the language and which belong to a neighbor language. The reason must be in the way how humans think and that they only want to cope with a small set of constructs at a time. As a result, not all link types are used for inter-notational links. Or at least: It would result in weird modeling languages. For example, the control flow between process steps should be part of the the same modeling language that defines the process steps.