Towards a Well-Founded Theory for Multi-Level Conceptual Modelling

Multi-level conceptual modelling addresses the representation of subject domains dealing explicitly with multiple classification levels. Despite the recent advances in multi-level modelling techniques, we believe that many challenges in multi-level conceptual modelling still stem from the lack of theory that: (i) formally characterizes the nature of classification levels, and (ii) precisely defines the structural relations that may occur between elements of different classification levels. This work aims to fill this gap by proposing an axiomatic theory that can be considered a reference toplevel ontology for types in multi-level conceptual modelling. The theory provides the modeller with basic concepts and patterns to articulate domains that require multiple levels of classification as well as to inform the development of well-founded languages for multi-level conceptual modelling. The theory includes intra-level structural relations that are used to define expressive multi-level models and cross-level relations that allow us to account for and incorporate the different notions of power type in the literature. Since all the relations in the theory are ultimately explained in terms of instantiation between entities of adjacent levels, it is capable to harmonize power type and clabject-based approaches.