Formalization of the unifying metamodel of UML, EER, and ORM

Last year Pablo Fillottrani and I introduced an ontology-driven unifying metamodel of the static, structural, entities of UML Class Diagrams (v2.4.1), ER, EER, ORM, and ORM2 in [1,2], which was informally motivated and described here. This now also includes the constraints and we have formalised it in First Order Predicate Logic to put some precision to the UML Class Diagram fragments and their associated textual constraints, which is described in the technical report of the metamodel formalization [3]. Besides having such precision for the sake of it, it is also useful for automated checking of inter-model assertions and computing model transformations, which we illustrated in our RuleML’14 paper earlier this year [4] (related blog post).

The ‘bummer’ of the formalization is that it probably requires an undecidable language, due to having formulae with five variables, counting quantifiers, and ternary predicates (see section 2.11 of the tech report for details). To facilitate various possible uses nevertheless, we therefore also made a slightly simpler OWL version of it (the modelling decisions are described in Section 3 of the technical report). Having that OWL version, it was easy to also generate a verbalisation of the OWL version of the metamodel (thanks to SWAT NL Tools) so as to facilitate reading of the ontology by the casually interested reader and the very interested one who doesn’t like logic.

Although our DST/MINCyT-funded South Africa-Argentina scientific collaboration project (entitled Ontology-driven unification of conceptual data modelling languages) is officially in its last few months by now, more results are in the pipeline, which I hope to report on shortly.

References

[1] Keet, C.M., Fillottrani, P.R. Toward an ontology-driven unifying metamodel for UML Class Diagrams, EER, and ORM2. 32nd International Conference on Conceptual Modeling (ER’13). 11-13 November, 2013, Hong Kong. Springer LNCS vol 8217, 313-326.

[2] Keet, C.M., Fillottrani, P.R. Structural entities of an ontology-driven unifying metamodel for UML, EER, and ORM2. 3rd International Conference on Model & Data Engineering (MEDI’13). September 25-27, 2013, Amantea, Calabria, Italy. Springer LNCS (in print).

[3] Fillottrani, P.R., Keet, C.M. KF metamodel formalization. Technical report, Arxiv.org http://arxiv.org/abs/1412.6545. Dec 19, 2014, 26p.

[4] Fillottrani, P.R., Keet, C.M. Conceptual Model Interoperability: a Metamodel-driven Approach. 8th International Web Rule Symposium (RuleML’14), A. Bikakis et al. (Eds.). Springer LNCS 8620, 52-66. August 18-20, 2014, Prague, Czech Republic.

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Towards a metamodel for conceptual data modeling languages

There are several conceptual data modelling languages one can use to develop a conceptual data model that should capture the subject domain of the application area in an implementation-independent way. Complex software development may need to leverage the strengths of each language yet have the need for interoperability between the software components; e.g., an application layer object-oriented software design in a UML Class diagram that needs to be able to talk to the EER diagram for a relational database. Or one is at a state where there are already several conceptual data models for different applications, but they need to be integrated (or at least made compatible). For various reasons, each of these models may well be represented in a different language, such as in UML, EER, ORM, MADS, Telos etc. Superficially, these languages all seem quite similar, even though they are known to be distinct in ‘a few’ features, such as that UML Class Diagrams typically have methods, but EER does not.

To adequately deal with such scenarios, we need not a comparison of language features, but a unification to foster interoperability. However, no unifying framework exists that respects all of their language features. In addition, one may wonder about questions such as: where are the real commonalities ontologically, what is fundamentally different, and what is the same in underlying idea or meaning but only looks different on the surface? We—Pablo Fillottrani (with the Universidad Nacional Del Sur in Argentina) and I—aim to fill this gap.

As a first step, we designed a common, ontology-driven, metamodel[1] of the static, structural, components of ER, EER, UML v2.4.1, ORM, and ORM2, in such a way that each language is strictly a fragment of the encompassing metamodel. In the meantime, we also have developed the metamodel for the constraints, but for now, the results of the metamodel for the static, structural, components have been accepted at the 32nd International Conference on Conceptual Modeling (ER’13) [1] and 3rd International Conference on Model & Data Engineering (MEDI’13) [2]. There is no repetition among the papers; it merely has been split up into two papers because of page limitations of conference proceedings and the amount of results we had.

The ER’13 paper [1] presents an overview on the core entities and constraints, and an analysis on roles and relationships, their interaction with predicates, and attributes and value types (which we refine with the notion of dimensional attribute). The MEDI’13 paper [2] focuses more on all the structural components, and covers a discussion on classes/concepts, subsumption, aggregation, and nested entity types.

(Warning: spoiler alert…) Perhaps surprisingly, the intersection of all the features in the selected languages is rather small: role, relationship (including subsumption), and object type. The attributions—attributes, value types—are represented differently, but they aim to represent the same underlying idea of attributive properties, and several implicit aspects, such as dimensional attribute and its reusability and relationship versus predicate, have been made explicit. Regarding constraints, only disjointness, completeness, mandatory, object cardinality, and the subset constraint appear in the three language families. The two overview figures in the paper have the classes colour-coded to give an easier overview on how many of the elements are shared across languages, and the appendix contains a table/list of terminology across UML, EER and ORM2, like that UML’s “association” and EER’s “relationship” denote the same kind of thing.

This also received attention in the UKZN e-news letter here, which combined the announcement of the ER’13 paper with my participation in the Dagstuhl seminar on Reasoning over Conceptual Schemas last May, the DST/NRF funded South Africa – Argentina bi-lateral project on the unification of conceptual modelling languages, and Pablo’s visit to UKZN the previous two weeks.

References

[1] Keet, C.M., Fillottrani, P.R. Toward an ontology-driven unifying metamodel for UML Class Diagrams, EER, and ORM2. 32nd International Conference on Conceptual Modeling (ER’13). 11-13 November, 2013, Hong Kong. Springer LNCS (in print).

[2] Keet, C.M., Fillottrani, P.R. Structural entities of an ontology-driven unifying metamodel for UML, EER, and ORM2. 3rd International Conference on Model & Data Engineering (MEDI’13). September 25-27, 2013, Amantea, Calabria, Italy. Springer LNCS (in print).

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[1] the term “metamodel” is used here in the common usage of the term in the literature, but, more precisely, we have a conceptual model that represents the entities and the constraints on their usage in a conceptual data model; e.g., it states that each relationship (association) is composed of at least two roles (association ends), that a nested entity type objectifies one relationship, that a multi-valued attribute is an attribute, and so on.