Multi-Layer Modeling (MLM)

Research in knowledge and ontology engineering is experiencing an ongoing effort to extend Conceptual Modeling (CM) to Meta-Level Modeling (MLM). The goal is to achieve greater expressiveness, lower memory requirements and less complex models with a minimal set of modeling elements. To accomplish their task, ontologies often need to represent beside classes (e.g., the class Car) and their instances (e.g., the Aston Martin driven by James Bond in Goldfinger) types of classes (e.g., Car_Model Aston Martin DB5). MLM is essentially about the interplay of classes and class types and how to assign values to attributes (DPs) of classes. The problem is that after merging a class Car with its powertype Car_Model, powertype attributes become class attributes. For example, the Car_Model attributes producedUnits and YearOfDesign become attributes of the Car class. As a result, it is necessary to introduce rules that govern the inheritance of attributes and values to subclasses and instances. For example, it should not be possible to inherit the YearOfDesign of the car model to car instances. These rules should be easy to learn and to master. Often, MLM methods introduce annotations within classes such as potency that determine how and to what extent attributes and their values are inherited, or to what extend attribute-value pairs are propaged down an instantiation chain. Thus, the goal of our study is to provide an MLM methodology that is more expressive while allowing for streamlined modeling.

Multi-Level Modeling, also known as hierarchical modeling, is commonly used in statistical analysis and machine learning to analyze data that is structured hierarchically or nested. Examples include students within courses, patients within hospitals, or repeated measurements taken over time on the same individuals. Meta-Level Modeling (MLM) refers to modeling at a higher level of abstraction. It is commonly used in computer science and software development, especially in Model-Driven Engineering (MDE). Both approaches deal with hierarchical structures, but in different contexts, namely, multi-level modeling in the context of data analysis and meta-level modeling in the context of model abstraction. And, both methods aim at improving decision-making, either by analyzing complex data or by providing robust model structures. In this paper, the focus is primarily on Meta-Level Modeling.

The key research question is: What instantiation rules and guidelines must be applied to Data Properties (DP) when moving from Conceptual Modeling (CM) to Meta-Level Modeling (MLM). How does this affect the modeling style of the ontologists? How can existing CM ontologies benefit from this, and what are the impacts?

The rest of this paragraph is organized as follows: In the Related Work, we discuss what approaches for Meta-Level Modeling (MLM) already exist and what shortcomings they have. The Preliminaries introduces the basic nomenclature we use and explains the main features of our minimal ontological top schema O4Top. Then, in the Data Property Types, we introduce four different types of data properties that we think are essential to fulfill the requirements of MLM. In the Examples, we first show how a typical conceptual model is transformed into a meta-level model and how powertypes can be subsumed under their base types. Second, we discuss, how MLM can also be applied to Object Properties (OP) and n-ary relations. In the Discussion, we analyze to what extent our methodology contributes to fulfilling the criteria for Meta-Level Modeling, and how metadata can be managed more systematically. We also discuss the savings potential of our method. In addition, we discuss how the multi-level features postulated by Fonseca et al. [FoAl2021] are satisfied. Finally, in the Results, we summarize the results and advantages of our approach.