Multi-level modeling (MLM)  represents a significant extension to the traditional two-level object-oriented paradigm with the potential to improve upon the utility, reliability, and complexity of models. Different from conventional approaches, MLM approaches allow for an arbitrary number of classification levels and introduce other concepts that foster expressiveness, reuse, and adaptability. A key aspect of the MLM paradigm is the use of entities (so-called clabjects) that are simultaneously types and instances , a feature which has consequences for conceptual modeling, for language engineering, and for the model-based development of software-intensive systems. MLM facilitates also deep instantiation , which, in contrast to shallow instantiation, allows model elements at a level to not only specify a scheme for elements at the next lower level but also to specify schemes for elements located at levels further down in the hierarchy. Different MLM approaches use different techniques to control and maintain this kind of instantiation. In Potency-based approaches [6, 8], for instance, a natural number (potency) is assigned to each model element indicating how many levels down in the hierarchy that element can be instantiated. Different variants of potency have been proposed to satisfy practical requirements, such as leap potency (facilitating jumps over levels) and depth (enforcing the last level at which an element may be instantiated).
While MLM collects a group of modeling features under one umbrella term, it has also fertilized interesting discussions regarding some of its basic modeling constructs, the principles behind levels, and the mechanisms used for controlling deep instantiation.
The MULTI workshop series is providing a forum for the MLM community to address the foundations of MLM approaches and support future developments through better modeling languages, tools, methods, and guidelines. The workshop calls have encouraged the presentation of case studies and tool demonstrations as well as novel concepts, implementation approaches, formalisms, controversial positions, and requirements for evaluation criteria. In the workshops, successful applications of MLM have been reported in domains such as software engineering, process modeling, enterprise modeling, industrial automation engineering, smart cities, and building information modeling. Furthermore, multiple common challenges, e.g., the bicycle challenge  and the process challenge , have been proposed as case studies in order to compare MLM approaches. Challenge participants were asked to employ an MLM approach to represent a domain that was initially described in natural language.
These initiatives have brought together researchers and practitioners in the area of MLM, specifically interested in developing conceptual modeling, domain-specific languages, database systems, and ontologies, to discuss synergies, common problems, and solutions of the different engineering disciplines, tool building concerns and techniques, and importantly, the vision for the future of MLM.
The Model-Driven Engineering (MDE) community has long embraced the need for MLM. Since the first MULTI workshop on MLM in 2014, a series of 8 workshop editions were co-located with the flagship conference in MDE: the International Conference on Model Driven Engineering Languages and Systems (MODELS). Many articles relying on MLM principles have been published in the Software and Systems Modeling (SoSyM) journal, and in a special issue of the EMISA journal. Furthermore, a Dagstuhl Seminar  in 2017 was organized and an increasing number of tools and languages have been proposed over the last years  including DPF workbench, GModel, Melanee, MetaDepth, MultEcore, Nivel, OMME, ML2, and XModeller.
This theme section continues this development of MLM by promoting and disseminating recent results in this field. It covers both papers on the foundations and on the applications of MLM. In total, 7 submissions—including one expert voice paper—were accepted for publication after a thorough peer-reviewing process.
Ulrich Frank, in his expert voice paper “Multi-level modeling: cornerstones of a rationale—comparative evaluation, integration with programming languages, and dissemination strategies” presents a comprehensive rationale of MLM including a systematic assessment of its prospects, promising applications of MLM in business information systems engineering, and future research perspectives.
Ferenc Somogyi, Gergely Mezei, Zoltán Theisz, Sándor Bácsi, and Dániel Palatinszky, in their paper “Playground for multi-level modeling constructs” present the MLM Playground, which is a validating modeling environment for MLM research. For instance, based on this modeling environment, one can experiment with different MLM language concepts in an agile way to study their relationships.
Mira Balaban, Igal Khitron, and Azzam Maraee, in their paper “Accidental complexity in multilevel modeling revisited” focus on the role of the context of type-instance structures within MLM architectures. They analyze factors of accidental complexity in multi-level models, provide quantitative metrics for capturing these factors, and show how these metrics are applied for guiding the transformations of multi-level models to reach better MLM architectures.
Thomas Kühne, in his paper “Multi-dimensional multi-level modeling” presents a novel multi-dimensional MLM approach based on the notion of orthogonal ontological classification. The resulting approach supports domain modeling with minimal complexity, systematic separation of concerns, and sanity-checking of the resulting models to avoid inconsistencies.
Alejandro Rodriguez, Francisco Duran, and Larsn Kristensen, in their paper “Simulation and analysis of MultEcore multi-level models based on rewriting logic” present a rich infrastructure for defining the structure and the operational semantics of MLM hierarchies which enables the simulation and analysis of such hierarchies. They define a rewriting logic semantics in Maude for MLM hierarchies specified in their tool MultEcore.
Bernd Neumayr and Michael Schrefl, in their paper “Domain object hierarchies inducing multi-level models” introduce the deep domain object MLM approach in which subclasses and metaclasses are induced by, and integrated with, the part-whole pattern which is a basic requirement for conceptualizing domain objects hierarchies.
Suilen H. Alvarado, Alejandro Cortiñas, Miguel R. Luaces, Oscar Pedreira, and Angeles S. Places, in their paper “Multilevel modeling of geographic information systems based on international standards” present an evaluation of potential benefits of MLM based on four representative scenarios, and conclude that an MLM approach is more appropriate for the investigated scenarios than a classical two-level metamodeling approach.
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First, we are thankful to the authors of papers presented at the MULTI workshop, and especially to those who submitted papers to this theme section. We also thank our reviewers for the timely manner in which they assisted in improving the selected papers. We would also like to thank all co-organizers, PC members, and SC members of previous MULTI workshop editions. Finally, we would like to express our gratitude to the SoSyM editorial office, specifically to Martin Schindler and Bernhard Rumpe who were always very helpful and supportive.
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Rutle, A., Wimmer, M. Guest editorial to the theme section on multi-level modeling. Softw Syst Model 21, 447–449 (2022). https://doi.org/10.1007/s10270-022-00987-1