A Typed Approach for Contextualizing the Part-Whole Relation

  • Richard Dapoigny
  • Patrick Barlatier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8175)


In the domain of knowledge representation as well as in Conceptual Modeling, representing part-whole relations is a long-stand-ing challenging problem. Most approaches addressing this issue rely on a set-theoretical framework, but many difficulties remain especially for disambiguating transitivity. In mathematical logic and program checking, dependent type theories have proved to be appealing but so far, they have been little applied in the formalization of knowledge. To bridge this gap, we represent part-of structures in a dependently-typed framework with the purpose of enhancing expressiveness through an explicit introduction of properties characterizing the context. We show that the dependently typed language easily captures the notion of contextualized part-of with many examples.


Domain Ontology Type Approach Dependent Type Transitive Relation Contextual Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barlatier, P., Dapoigny, R.: A Type-Theoretical Approach for Ontologies: the Case of Roles. Applied Ontology 7(3), 311–356 (2012)Google Scholar
  2. 2.
    Jacobs, B.: Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics, vol. 141. Elsevier (1999)Google Scholar
  3. 3.
    Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. An EATCS series. Springer (2004)Google Scholar
  4. 4.
    Bittner, T., Smith, B.: A Theory of Granular Partitions. In: Duckham, M., Goodchild, M.F., Worboys, M. (eds.) Foundations of Geographic Information Science, ch. 7, pp. 124–125 (2003)Google Scholar
  5. 5.
    Bittner, R., Donelly, M., Smith, B.: Individuals, Universals, Collections: On the Foundational Relations of Ontology. Frontiers in Artificial Intelligence, vol. 114. IOS Press, Amsterdam (2010)Google Scholar
  6. 6.
    Casati, R., Varzi, A.C.: Parts and places: the structures of spatial representation. MIT Press (1999)Google Scholar
  7. 7.
    Cirstea, H., Coquery, E., Drabent, W., Fages, F., Kirchner, C., Maluszynski, J., Wack, B.: Types for Web Rule Languages: a preliminary study, technical report A04-R-560, PROTHEO - INRIA Lorraine - LORIA (2004)Google Scholar
  8. 8.
    Dapoigny, R., Barlatier, P.: Modeling Contexts with Dependent Types. Fundamenta Informaticae 104(4), 293–327 (2010)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Dapoigny, R., Barlatier, P.: Towards Ontological Correctness of Part-whole Relations with Dependent Types. In: Procs. of the Sixth Int. Conference (FOIS 2010), pp. 45–58 (2010)Google Scholar
  10. 10.
    Dapoigny, R., Barlatier, P.: Modeling Ontological Structures with Type Classes in Coq. In: Pfeiffer, H.D., Ignatov, D.I., Poelmans, J., Gadiraju, N. (eds.) ICCS 2013. LNCS, vol. 7735, pp. 135–152. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Angelov, K., Enache, R.: Typeful Ontologies with Direct Multilingual Verbalization. In: Rosner, M., Fuchs, N.E. (eds.) CNL 2010. LNCS(LNAI), vol. 7175, pp. 1–20. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Gangemi, A., Guarino, N., Masolo, C., Oltramari, A., Schneider, L.: Sweetening ontologies with DOLCE. In: Gómez-Pérez, A., Benjamins, V.R. (eds.) EKAW 2002. LNCS(LNAI), vol. 2473, pp. 166–181. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Gerstl, P., Pribbenow, S.: Midwinters, end games, and body parts: a classification of part-whole relations. International Journal of Human-Computer Studies 43(5-6), 865–889 (1995)CrossRefGoogle Scholar
  14. 14.
    Guizzardi, G.: Ontological Foundations for Structural Conceptual Models, University of Twente, Centre for Telematics and Information Technology (2005)Google Scholar
  15. 15.
    Guizzardi, G., Masolo, C., Borgo, S.: In Defense of a Trope-Based Ontology for Conceptual Modeling: An Example with the Foundations of Attributes, Weak Entities and Datatypes. In: Embley, D.W., Olivé, A., Ram, S. (eds.) ER 2006. LNCS, vol. 4215, pp. 112–125. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Guizzardi, G.: The Problem of Transitivity of Part-Whole Relations in Conceptual Modeling Revisited. In: van Eck, P., Gordijn, J., Wieringa, R. (eds.) CAiSE 2009. LNCS, vol. 5565, pp. 94–109. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Guizzardi, G.: Representing Collectives and Their Members in UML Conceptual Models: An Ontological Analysis. In: Trujillo, J., et al. (eds.) ER 2010. LNCS, vol. 6413, pp. 265–274. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Howard, W.A.: The formulae-as-types notion of construction. In: To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pp. 479–490. Academic Press (1980)Google Scholar
  19. 19.
    Husserl, E.: Logische Untersuchungen. Zweiter Band, Untersuchungen zur Phänomenologie und Theorie der Erkenntnis. Niemeyer, Halle (1901); Eng. trans. by Findlay, J.N.: Logical Investigations, vol. 2. Routledge & Kegan Paul, London (1970)Google Scholar
  20. 20.
    Johansson, I.: On the Transitivity of the Parthood Relations. In: Relations and Predicates, pp. 161–181. Ontos-Verlag (2004)Google Scholar
  21. 21.
    Keet, C.M., Artale, A.: Representing and reasoning over a taxonomy of part-whole relations. Applied Ontology 3(1-2), 91–110 (2008)Google Scholar
  22. 22.
    Leśniewski, S.: Podstawy ogólnej teoryi mnogosci. I. Moskow: Prace Polskiego Kola Naukowego w Moskwie, Sekcya matematyczno-przyrodnicza (1916); English translation by Barnett, D. I.: Foundations of the General Theory of Sets. I, In: Leśniewski, S., Collected Works, Surma, S.J., Srzednicki, J., Barnett, D.I., Rickey, F.V. (eds.), vol. 1, pp. 129–173. Kulwer, Dordrecht (1992)Google Scholar
  23. 23.
    Luo, Z.: Computation and Reasoning, vol. 11. Oxford Science Publications (1994)Google Scholar
  24. 24.
    Masolo, C., Borgo, S., Gangemi, A., Guarino, N., Oltramari, A.: Ontology Library (D18), Laboratory for Applied Ontology-ISTC-CNR (2003)Google Scholar
  25. 25.
    Mylopoulos, J., Borgida, A., Jarke, M., Koubarakis, M.: Telos: Representing Knowledge About Information Systems. ACM Trans. on Information Systems 8(4), 325–362 (1990)CrossRefGoogle Scholar
  26. 26.
    Pribbenow, S.: Meronymic Relationships: From Classical Mereology to Complex Part-Whole Relations. In: Green, R., Bean, C.A. (eds.) The Semantics of Relationships, pp. 35–50. Kluwer, Dordretch (2002)CrossRefGoogle Scholar
  27. 27.
    Setzer, A.: Object-Oriented Programming in Dependent Type Theory. Trends in Functional Programming 7, 91–108 (2007)Google Scholar
  28. 28.
    Simons, P.: Parts: A Study in Ontology. Clarendon Press, Oxford (1987)Google Scholar
  29. 29.
    Varzi, A.C.: Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering 20(3), 259–286 (1996)CrossRefzbMATHGoogle Scholar
  30. 30.
    Vieu, L.: On the transitivity of functional parthood. Applied Ontology 1, 147–155 (2006)Google Scholar
  31. 31.
    Winston, M.E., Chaffin, R., Herrman, D.: A taxonomy of part-whole relations. Cognitive Science 11(4), 417–444 (1987)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Richard Dapoigny
    • 1
  • Patrick Barlatier
    • 1
  1. 1.LISTIC/Polytech’Annecy-ChambéryUniversity of SavoieAnnecy-le-vieux cedexFrance

Personalised recommendations