Abstract Model management is a central activity in Software Engineering. The most challenging aspect of model management is to keep inter-related models consistent with each other while they evolve. As a consequence, there is a lot of scientific activity in this area, which has produced an extensive body of knowledge, methods, results and tools. The majority of these approaches, however, are limited to binary inter-model relations; i.e. the synchronisation of exactly two models. Yet, not every multi-ary relation can be factored into a family of binary relations. In this paper, we propose and investigate a novel comprehensive system construction, which is able to represent multi-ary relations among multiple models in an integrated manner and thus serves as a formal foundation for artefacts used in consistency management activities involving multiple models. The construction is based on the definition of partial commonalities among a set of models using the same language, which is used to denote the (local) models. The main theoretical results of this paper are proofs of the facts that comprehensive systems are an admissible environment for (i) applying formal means of consistency verification (diagrammatic predicate framework), (ii) performing algebraic graph transformation (weak adhesive HLR category), and (iii) that they generalise the underlying setting of graph diagrams and triple graph grammars.

The elegance of the single-pushout (SPO) approach to graph transformations arises from substituting total morphisms by partial ones in the underlying category. SPO's applicability depends on the durability of pushouts after this transition. There is a wide range of work on the question when pushouts exist in categories with partial morphisms starting with the pioneering work of Löwe and Kennaway and ending with an essential characterisation in terms of an exactness property (for the interplay between pullbacks and pushouts) and an adjointness condition (w.r.t. inverse image functions) by Hayman and Heindel. Triple graphs and graph diagrams are frameworks to synchronise two or more updatable data sources by means of internal mappings, which identify common sub-structures. Comprehensive systems generalise these frameworks, treating the network of data sources and their structural inter-relations as a homogeneous comprehensive artefact, in which partial maps identify commonalities. Although this inherent partiality produces amplified complexity, we can show that Heindel's characterisation still yields existence of pushouts in the category of comprehensive systems and reflective partial morphisms and thus enables computing by typed SPO graph transformation.

Model management is a central activity in Software Engineering. The most challenging aspect of model management is to keep models consistent with each other while they evolve. As a consequence, there has been increasing activity in this area, which has produced a number of approaches to address this synchronization challenge. The majority of these approaches, however, is limited to a binary setting; i.e. the synchronization of exactly two models with each other. A recent Dagstuhl seminar on multidirectional transformations made it clear that there is a need for further investigations in the domain of general multiple model synchronization simply because not every multiary consistency relation can be factored into binary ones. However, with the help of an auxiliary artifact, which provides a global view over all models, multiary synchronization can be achieved by existing binary model synchronization means. In this paper, we propose a novel comprehensive system construction to produce such an artifact using the same underlying base modelling language as the one used to define the models. Our approach is based on the definition of partial commonalities among a set of aligned models. Comprehensive systems can be shown to generalize the underlying categories of graph diagrams and triple graph grammars and can efficiently be implemented in existing tools.