Object-Role Modeling (ORM) is a so-called “true” conceptual modelling language in the sense that it is independent of the application scenario and it has been mapped into both UML class diagrams and ER . That is, ORM and its successor ORM2 can be used in the conceptual analysis stage for database development, application software development, requirements engineering, business rules, and other areas [1-5]. If we can reason over such ORM conceptual data models, then we can guarantee the model (i.e., first order logic theory) is satisfiable and consistent, so that the corresponding application based on it definitely does behave correctly with respect to its specification (I summarised a more comprehensive argumentation and examples earlier). And, well, from a push-side: it widens the scope of possible scenarios where to use automated reasoners.
Various strategies and technologies are being developed to reason over conceptual data models to meet the same or slightly different requirements and aims. An important first distinction is between the assumption that modellers should be allowed to keep total freedom to model what they deem necessary to represent and subsequently put constraints on which parts can be used for reasoning or accept slow performance versus the assumption that it is better to constrain the language a priori to a subset of first order logic so as to achieve better performance and a guarantee that the reasoner terminates. The former approach is taken by Queralt and Teniente  using a dependency graph of the constraints in a UML Class Diagram + OCL and by first order logic (FOL) theorem provers. The latter approach is taken by [7-15] who experiment with different techniques. For instance, Smaragdakis et al and Kaneiwa et al [7-8] use special purpose reasoners for ORM and UML Class Diagrams, Cabot et al and Cadoli et al [9-10] encode a subset of UML class diagrams as a Constraint Satisfaction Problem, and [11-16] use a Description Logic (DL) framework for UML Class Diagrams, ER, EER, and ORM.
Perhaps not surprisingly, I also took the DL approach on this topic, on which I started working in 2006. I had put the principal version of the correspondence between ORM and the DL language DLRifd online on arXiv in February 2007 and got the discussion of the fundamental transformation problems published at DL’07 . Admittedly, that technical report won’t ever win the beauty prize for its layout or concern for readability. In the meantime, I have corrected the typos, improved on the readability, proved correctness of encoding, and updated the related research with the recent works. On the latter, it also contains a discussion of a later, similar, attempt by others and the many errors in it. On the bright side: addressing those errors helps explaining the languages and trade-offs better (there are advantages to using a DL language to represent an ORM diagram, but also disadvantages). This new version (0702089v2), entitled “Mapping the Object-Role Modeling language ORM2 into Description Logic language DLRifd”  is now also online at arXiv.
As appetizer, here’s the abstract:
In recent years, several efforts have been made to enhance conceptual data modelling with automated reasoning to improve the model’s quality and derive implicit information. One approach to achieve this in implementations, is to constrain the language. Advances in Description Logics can help choosing the right language to have greatest expressiveness yet to remain within the decidable fragment of first order logic to realise a workable implementation with good performance using DL reasoners. The best fit DL language appears to be the ExpTime-complete DLRifd. To illustrate trade-offs and highlight features of the modelling languages, we present a precise transformation of the mappable features of the very expressive (undecidable) ORM/ORM2 conceptual data modelling languages to exactly DLRifd. Although not all ORM2 features can be mapped, this is an interesting fragment because it has been shown that DLRifd can also encode UML Class Diagrams and EER, and therefore can foster interoperation between conceptual data models and research into ontological aspects of the modelling languages.
And well, for those of you who might be disappointed that not all ORM features can be mapped: computers have their limitations and people have a limited amount of time and patience. To achieve ‘scalability’ of reasoning over initially large theories represented in a very expressive language, modularisation of the conceptual models and ontologies is one of the lines of research. But it is a separate topic and not quite close to implementation just yet.
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