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A Comprehensive Formal Theory for Multi-level Conceptual Modeling

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Conceptual Modeling (ER 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10650))

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Abstract

Multi-level modeling extends the conventional two-level classification scheme to deal with subject domains in which classes are also considered instances of other classes. In the past, we have explored theoretical foundations for multi-level conceptual modeling and proposed an axiomatic theory for multi-level modeling dubbed MLT. MLT provides concepts for multi-level modeling along with a number of rules to guide the construction of sound multi-level conceptual models. Despite the benefits of MLT, it is still unable to deal with a number of general notions underlying conceptual models (including the notions used in its own definition). In this paper, we present an extension of MLT to deal with these limitations. The resulting theory (called MLT*) is novel in that it combines a strictly stratified theory of levels with the flexibility required to model abstract notions that defy stratification into levels such as a universal “Type” or, even more abstract notions such as “Entity” and “Thing”.

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Notes

  1. 1.

    See https://github.com/nemo-ufes/mlt-ontology.

  2. 2.

    See [10] for a refinement of identity and specialization concerning modal distinctions.

References

  1. Atkinson, C., Kühne, T.: Meta-level independent modelling. In: International Workshop on Model Engineering at 14th European Conference on Object-Oriented Programming, pp. 1–4 (2000)

    Google Scholar 

  2. Atkinson, C., Kühne, T.: Reducing accidental complexity in domain models. Softw. Syst. Model. 7, 345–359 (2008)

    Article  Google Scholar 

  3. Atkinson, C., Gerbig, R.: Melanie: multi-level modeling and ontology engineering environment. In: Proceedings of the 2nd International Master Class on MDE Modeling Wizards. ACM (2012)

    Google Scholar 

  4. Atkinson, C., Gerbig, R., Kühne, T.: Comparing multi-level modeling approaches. In: Proceedings of the 1st International Workshop on Multi-Level Modelling (2014)

    Google Scholar 

  5. Brasileiro, F., Almeida, J.P.A., Carvalho, V.A., Guizzardi, G.: Expressive multi-level modeling for the semantic web. In: Groth, P., Simperl, E., Gray, A., Sabou, M., Krötzsch, M., Lecue, F., Flöck, F., Gil, Y. (eds.) ISWC 2016 Part I. LNCS, vol. 9981, pp. 53–69. Springer, Cham (2016). doi:10.1007/978-3-319-46523-4_4

    Chapter  Google Scholar 

  6. Brasileiro, F., Almeida, J.P.A., Carvalho, V.A., Guizzardi, G.: Applying a multi-level modeling theory to assess taxonomic hierarchies in Wikidata. In: Proceedings of the Wiki Workshop 2016 at 25th International Conference on Companion on World Wide Web, pp. 975–980 (2016)

    Google Scholar 

  7. Cardelli, L.: Structural subtyping and the notion of power type. In: Proceedings of the 15th ACM Symposium of Principles of Programming Languages, pp. 70–79 (1988)

    Google Scholar 

  8. Carvalho, V.A., Almeida, J.P.A.: A semantic foundation for organizational structures: a multi-level approach. IEEE EDOC 2015, 50–59 (2015)

    Google Scholar 

  9. Carvalho, V.A., Almeida, J.P.A., Fonseca, C.M., Guizzardi, G.: Extending the foundations of ontology-based conceptual modeling with a multi-level theory. In: Johannesson, P., Lee, M.L., Liddle, S.W., Opdahl, A.L., López, Ó.P. (eds.) ER 2015. LNCS, vol. 9381, pp. 119–133. Springer, Cham (2015). doi:10.1007/978-3-319-25264-3_9

    Chapter  Google Scholar 

  10. Carvalho, V.A., Almeida, J.P.A.: Towards a well-founded theory for multi-level conceptual modeling. Softw. Syst. Model. 10, 1–27 (2016). Springer

    Google Scholar 

  11. Carvalho, V.A., Almeida, J.P.A., Guizzardi, G.: Using a well-founded multi-level theory to support the analysis and representation of the powertype pattern in conceptual modeling. In: Nurcan, S., Soffer, P., Bajec, M., Eder, J. (eds.) CAiSE 2016. LNCS, vol. 9694, pp. 309–324. Springer, Cham (2016). doi:10.1007/978-3-319-39696-5_19

    Chapter  Google Scholar 

  12. Clark, T., Gonzalez-Perez, C., Henderson-Sellers, B.: A foundation for multi-level modelling. In: Proceedings of Workshop on Multi-Level Modelling, MODELS, pp. 43–52 (2014)

    Google Scholar 

  13. Foxvog, D.: Instances of instances modeled via higher-order classes. In: 28th German Conference on AI Foundational Aspects of Ontologies (FOnt 2005), pp. 46–54 (2005)

    Google Scholar 

  14. Frank, U.: Multilevel modeling. Bus. Inf. Syst. Eng. 6, 319–337 (2014)

    Article  Google Scholar 

  15. Gonzalez-Perez, C., Henderson-Sellers, B.: A powertype-based metamodelling framework. Softw. Syst. Model. 5, 72–90 (2006)

    Article  Google Scholar 

  16. Guizzardi, G.: Ontological Foundations for Structural Conceptual Models. University of Twente, Enschede (2005)

    MATH  Google Scholar 

  17. Henderson-Sellers, B.: On the Mathematics of Modeling, Metamodelling, Ontologies and Modelling Languages. Springer, Heidelberg (2012)

    Book  Google Scholar 

  18. Irvine, A.D., Deutsch, H.: Russell’s paradox. In: The Stanford Encyclopedia of Philosophy (2016). https://plato.stanford.edu/archives/win2016/entries/russell-paradox/

  19. Jackson, D.: Software Abstractions: Logic, Language and Analysis. The MIT Press, Cambridge (2006)

    Google Scholar 

  20. Jarke, M., et al.: ConceptBase – a deductive object base for meta data management. J. Intell. Inf. Syst. 4, 167–192 (1995)

    Article  Google Scholar 

  21. Jeusfeld, M.A., Neumayr, B.: DeepTelos: multi-level modeling with most general instances. In: Comyn-Wattiau, I., Tanaka, K., Song, I.-Y., Yamamoto, S., Saeki, M. (eds.) ER 2016. LNCS, vol. 9974, pp. 198–211. Springer, Cham (2016). doi:10.1007/978-3-319-46397-1_15

    Chapter  Google Scholar 

  22. de Lara, J., Guerra, E.: Deep meta-modelling with MetaDepth. In: Proceedings of the 48th International Conference, TOOLS 2010, Málaga, Spain (2010)

    Google Scholar 

  23. de Lara, J., et al.: Extending deep meta-modelling for practical model-driven engineering. Comput. J. 57(1), 36–58 (2014)

    Article  Google Scholar 

  24. de Lara, J., Guerra, E., Cuadrado, J.S.: When and how to use multilevel modelling. ACM Trans. Softw. Eng. Methodol. 24, 1–46 (2014)

    Article  Google Scholar 

  25. Masolo, C., Borgo, S., Gangemi, A., Guarino, N., Oltramari, A.: Ontology library. In: WonderWeb Deliverable D18 (2003)

    Google Scholar 

  26. Mayr, E.: The Growth of Biological Thought: Diversity, Evolution, and Inheritance. The Belknap Press, Cambridge (1982)

    Google Scholar 

  27. Menzel, C.: Knowledge representation, the world wide web, and the evolution of logic. Synthese 182, 269–295 (2011)

    Article  MathSciNet  Google Scholar 

  28. Mylopoulos, J., et al.: Telos: representing knowledge about information systems. ACM Trans. Inf. Syst. (TOIS) 8, 325–362 (1990)

    Article  Google Scholar 

  29. Neumayr, B., Grün, K., Schrefl, M.: Multi-level domain modeling with M-objects and M-relationships. In: Proceedings of 6th Asia-Pacific Conf. Conceptual Modeling, New Zealand (2009)

    Google Scholar 

  30. Odell, J.: Power types. J. Object-Oriented Program. 7(2), 8–12 (1994)

    Google Scholar 

  31. W3C: RDF Schema 1.1 (2014). https://www.w3.org/TR/2014/REC-rdf-schema-20140225/

  32. W3C: OWL 2 Web Ontology Language-Document Overview (Second Edition) (2012). https://www.w3.org/TR/2012/REC-owl2-syntax-20121211

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Acknowledgements

This research is funded by CNPq (grants numbers 311313/2014-0, 461777/2014-2 and 407235/2017-5), CAPES (23038.028816/2016-41) and FAPES (69382549). Claudenir M. Fonseca is funded by CAPES. We thank Giancarlo Guizzardi for fruitful discussions in topics related to this paper.

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Authors and Affiliations

  1. Ontology and Conceptual Modeling Research Group (NEMO), Federal University of Espírito Santo (UFES), Vitória, ES, Brazil

    João Paulo A. Almeida & Claudenir M. Fonseca

  2. Research Group in Applied Informatics, Informatics Department, Federal Institute of Espírito Santo (IFES), Colatina, ES, Brazil

    Victorio A. Carvalho

Authors
  1. João Paulo A. Almeida
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  2. Claudenir M. Fonseca
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  3. Victorio A. Carvalho
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Corresponding author

Correspondence to João Paulo A. Almeida .

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Editors and Affiliations

  1. University of Klagenfurt, Klagenfurt, Austria

    Heinrich C. Mayr

  2. Free University of Bozen-Bolzano, Bozen-Bolzano, Italy

    Giancarlo Guizzardi

  3. Victoria University of Wellington, Wellington, New Zealand

    Hui Ma

  4. Valencia University of Technology, Valencia, Spain

    Oscar Pastor

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Almeida, J.P.A., Fonseca, C.M., Carvalho, V.A. (2017). A Comprehensive Formal Theory for Multi-level Conceptual Modeling. In: Mayr, H., Guizzardi, G., Ma, H., Pastor, O. (eds) Conceptual Modeling. ER 2017. Lecture Notes in Computer Science(), vol 10650. Springer, Cham. https://doi.org/10.1007/978-3-319-69904-2_23

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  • DOI: https://doi.org/10.1007/978-3-319-69904-2_23

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