# First tractable encoding of ORM conceptual data models

For (relatively) many years I’ve been focusing on as-expressive-as-possible languages to represent information and knowledge, including the computationally impractical full first order logic, because one would/should want to be as precise as possible and required to represent the subject domain in an ontology and universe of discourse for the application in a conceptual data model. After all, one can always throw out the computationally unpleasant constructs later during the implementation stage, if the ontology or conceptual data model is intended for use at runtime, such as OBDA [1], test data generate for verification [2], and in the query compilation stage in RDBMSs [3]. The resulting slimmed theories/models may be different for different applications, but then at least the set of slimmed theories/models share their common understanding.

So, now I ventured in that area, not because there’s some logic x and conceptual modeling language y has to be forced into it, but it actually appears that many fancy construct/features are not used in publicly available conceptual data models anyway (see data set and xls with some analysis). The timing of the outcome of the analysis of the data set coincided with David Toman’s visit to UCT as part of his sabbatical and Pablo Fillottrani’s visit, who enjoyed the last exchange of our bi-lateral project on the unification of conceptual data modelling languages (project page). To sum up the issue we were looking at: the need for run-time usage of conceptual data models requires a tractable logic-based reconstruction of the conceptual models (i.e., in at most PTIME), which appeared to hardly exist or miss constructs important for conceptual models (regardless whether that was ORM, EER or UML Class Diagrams), or both.

The solution ended up to be a logic-based reconstruction for most of ORM2 using the $\mathcal{CFDI}_{nc}^{\forall -}$ Description Logic, which also happens to be the first tractable encoding of (most of) ORM/ORM2. With this logic, several features important for conceptual models (i.e., occur relatively often) do have their proper encoding in the logic, notably n-aries, complex identification constraints, and n-ary role subsumption. The, admittedly quite tedious, mapping

Low resolution and small version of our DL15 poster summarising the contributions.

captures over 96% of the constructs used in practice in the set of 33 ORM diagrams we analysed (see data set). Further, the results are easily transferable to EER and UML Class diagrams, with an even greater coverage. The results (and comparison with related works) are presented in our recently accepted paper at the 28th International Workshop on Description Logics (DL’15) that will take place form 7 to 11 June in Athens, Greece.

The list of accepted papers of DL’15 is available, listing 21 papers with long presentations, 16 papers with short presentation, and 26 papers with poster presentations. David will present our results in the poster session, as it’s probably of more relevance in the conceptual modelling community (and I’ll be marking exams then), and some other accepted papers cover more new ground, such as casting schema.org as a description logic, temporal query answering in EL, exact learning of ontologies, and more. The proceedings is will be online on CEUR-WS in the upcoming days as volume 1350. I’ve added a mini version of our poster on the right. I tried tikzposter, as they look really cool, but it doesn’t support figures (other than those made in latex), so I resorted to ppt (that doesn’t support math), wondering why these issues haven’t been solved by now.

References

[1] Calvanese, D., Keet, C.M., Nutt, W., Rodriguez-Muro, M., Stefanoni, G. Web-based Graphical Querying of Databases through an Ontology: the WONDER System. ACM Symposium on Applied Computing (ACM SAC’10), March 22-26 2010, Sierre, Switzerland. pp 1389-1396.

[2] Toman, D., Weddell, G.E.: Fundamentals of Physical Design and Query Compilation. Synthesis Lectures on Data Management, Morgan & Claypool  Publishers (2011)

[3] Smaragdakis, Y., Csallner, C., Subramanian, R.: Scalable satisfiability checking and test data generation from modeling diagrams. Automation in Software Engineering 16, 73–99 (2009)

[4] Fillottrani, P.R., Keet, C.M., Toman, D. Polynomial encoding of ORM conceptual models in $\mathcal{CFDI}_{nc}^{\forall -}$. 28th International Workshop on Description Logics (DL’15). CEUR-WS vol xx., 7-10 June 2015, Athens, Greece.