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.


[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, 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.

FAIR’14 and ‘modelling relationships’ tutorial

After a weekend of ‘loadshedding’ (one of those South African euphemisms) I’m posting a few notes on the Forum on Artificial Intelligence Research 2014 (FAIR’14) that took place from 3-5 Dec 2014 at Stellenbosch University, which was organised by CAIR and co-located with the FASTAR/Espresso Workshop 2014, which, in turn, was co-located with PRASA, AFLaT, and RobMech 2014 in Cape Town. FAIR’14 consisted of a presentation by Sergei Obiedkov of the Higher School of Economics, Russia, a tutorial on modelling relationships in ontologies by me, and a course on computational social choice theory by Ulle Endriss from the ILLC, University of Amsterdam, The Netherlands.

While not quite relevant to my current research except for judgement aggregation at the end (for crowdsourcing), Ulle’s course was one of those events that made me think “[why didn’t/if only] I was exposed to this material before?!”, when I had to make choices as to what to study and specialise in (though, admitted, once knowing about the math with game theory and applying that to peace negotiations in my MA pdf, I still went on in CS with KR&R and ontologies). Ulle’s course combined socially relevant topics, such as the fair allocation of resources and voting systems, with solid, precise, logic- and math-based representations and computation. Besides the engaging content, he’s also good at teaching it. The content and slides are a condensed version of his MSc course on social choice theory and are available online here, which also has links to related reading material.

I tried to condense into 2 hours some aspects of modelling relationships in ontologies. It started with some problems and questions, proceeded to touching upon the nature of relations and some detail of the formal semantics, common relationships (with some detail about mereotopology), and closing with some practical modelling guidance and reasoner performance when modelling it one way or another. It being a tutorial, and not all participants had Protégé installed, I resorted to a peer instruction audience response system to incorporate interactively some questions about modelling some relationships. The slides are available online (though also here the text on the slides only partially reflect what I’ve talked about).

Other than that, there’s always the social component. Despite the weird time-warp that Stellenbosch town constitutes, it was really nice to catch up with former colleagues and to see the progress of postgrads of UKZN, to hear about the future of CAIR, and that it’s a small world even when meeting people new to me. And the food & wine was delicious. The train travel back to Cape Town took a bit longer than the schedule said it ought to be, but I recommend it nevertheless.