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Multi-dimensional multi-level modeling

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Abstract

The growth of multi-level modeling has resulted in an increase of level-organization alternatives which significantly differ from each other with respect to their underlying foundations and the well-formedness rules they enforce. Alternatives substantially diverge with respect to how level boundaries should govern instance-of relationships, what modeling mechanisms they employ, and what modeling principles they establish. In this article, I analyze how a number of multi-level modeling approaches deal with certain advanced modeling scenarios. In particular, I identify linear domain metamodeling, i.e., the requirement that all domain-induced instance-of relationships align with a single global level-hierarchy, as a source of accidental complexity. I propose a novel multi-dimensional multi-level modeling approach based on the notion of orthogonal ontological classification that supports modeling of domain scenarios with minimal complexity while supporting separation of concerns and sanity-checking to avoid inconsistent modeling choices.

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Notes

  1. The need for such resolution mechanisms is therefore a good justification for the use of multiple inheritance as an indirect way of supporting multiple classification, since the resolution can be achieved at the type level, rather than for each instance individually.

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Acknowledgements

I would like to thank Colin Atkinson for numerous debates which helped sharpen some of the ideas presented in this article and significantly informed their presentation. I would furthermore like to thank João Paulo Almeida and Victorio Carvalho for their work and a number of discussions which helped me form the ideas for this article. Finally, I would like to thank SoSyM’s anonymous reviewers whose comments further improved the presentation of this article.

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  1. Victoria University of Wellington, Wellington, New Zealand

    Thomas Kühne

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Correspondence to Thomas Kühne.

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Communicated by Adrian Rutle and Manuel Wimmer.

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Kühne, T. Multi-dimensional multi-level modeling. Softw Syst Model 21, 543–559 (2022). https://doi.org/10.1007/s10270-021-00951-5

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