Multi-level conceptual modeling: Theory, language and application

In many important subject domains, there are central real-world phenomena that span across multiple classification levels. In these subject domains, besides having the traditional type-level domain regularities (classes) that classify multiple concrete instances, we also have higher-order type-level regularities (metaclasses) that classify multiple instances that are themselves types. Multi-Level Modeling aims to address this technical challenge. Despite the advances in this area in the last decade, a number of requirements arising from representation needs in subject domains have not yet been addressed in current modeling approaches. In this paper, we address this issue by proposing an expressive multi-level conceptual modeling language (dubbed ML2). We follow a principled language engineering approach in the design of ML2, constructing its abstract syntax as to reflect a fully axiomatized theory for multi-level modeling (termed MLT*). We show that ML2 enables the expression of a number of multi-level modeling scenarios that cannot be currently expressed in the existing multi-level modeling languages. A textual syntax for ML2 is provided with an implementation in Xtext. We discuss how the formal theory influences the language in two aspects: (i) by providing rigorous justification for the language's syntactic rules, which follow MLT* theorems and (ii) by forming the basis for model simulation and verification. We show that the language can reveal problems in multi-level taxonomic structures, using Wikidata fragments to demonstrate the language's practical relevance.