Knowledge Representation and Formal Reasoning in Ontologies with Coq

  • Vasyl LenkoEmail author
  • Volodymyr Pasichnyk
  • Natalia Kunanets
  • Yuriy Shcherbyna
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 754)


The paper describes a modern type-theoretical approach to the knowledge representation and formal reasoning in ontologies. The current state and limitations of the adopted technology for reasoning in ontologies as well as the advantages of the proposed approach are highlighted. Curry-Howard correspondence and its role in the establishment of computational reasoning are emphasized. The main part is dedicated towards the representation of ontology elements in Coq proof assistant and the execution of a semi-automated reasoning over them.


Ontology Knowledge representation Formal reasoning Type theory Coq 


  1. 1.
    Dutant, J.: The legend of the justified true belief analysis. Phil. Perspect. 29(1), 95–145 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Baskarada, S., Koronios, A.: Data, Information, Knowledge, Wisdom (DIKW): a semiotic theoretical and empirical exploration of the hierarchy and its quality dimension. Australas. J. Inf. Syst. 18(1), 5–24 (2013)Google Scholar
  3. 3.
    Mabel, V.H., Selwyn, J.: A review on the knowledge representation models and its implications. Int. J. Inf. Technol. Comput. Sci. 8(10), 72–81 (2016). Scholar
  4. 4.
    Malhotra, M., Nair, T.R.G.: Evolution of knowledge representation and retrieval techniques. Int. J. Intell. Syst. Appl. (IJISA) 7(7), 18–28 (2015). Scholar
  5. 5.
    Feilmayr, C., Wöß, W.: An analysis of ontologies and their success factors for application to business. Data Knowl. Eng. 101, 1–23 (2016)CrossRefGoogle Scholar
  6. 6.
    Gruber, T.: A translation approach to portable ontology specifications. Knowl. Acquis. 5(2), 199–220 (1993)CrossRefGoogle Scholar
  7. 7.
    OWL 2 Web Ontology Language Document Overview (Second Edition). Accessed 04 Dec 2017
  8. 8.
    Krötzsch, M., Simančik, F., Horrocks, I.: Description Logics. IEEE Intell. Syst. 29(1), 12–19 (2014)CrossRefGoogle Scholar
  9. 9.
    Yahiaoui, Y., Lehireche, A., Bouchiha, D.: Proposed representation approach based on description logics formalism. Int. J. Intell. Syst. Appl. 8(5), 1–9 (2016). Scholar
  10. 10.
    DL-Safe Rules. Accessed 04 Dec 2017
  11. 11.
    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)Google Scholar
  12. 12.
    Dapoigny, R., Barlatier, P.: Specifying well-formed part-whole relations in Coq. In: Hernandez, N., Jäschke, R., Croitoru, M. (eds.) ICCS 2014. LNCS, vol. 8577, pp. 159–173. Springer, Cham (2014)Google Scholar
  13. 13.
    Hafsi, M., Dapoigny, R., Bolon, P.: Toward a type-theoretical approach for an ontologically-based detection of underground networks. In: Zhang, S., Wirsing, M., Zhang, Z. (eds.) KSEM 2015. LNCS, vol. 9403, pp. 90–101. Springer, Cham (2015)Google Scholar
  14. 14.
    Paulin-Mohring, C.: Introduction to the calculus of inductive constructions. In: Delahaye, D., Paleo, B.W. (eds.) All about Proofs, Proofs for All. Mathematical Logic and Foundations. College Publications, London (2015)Google Scholar
  15. 15.
    The Univalent Foundations Program: Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for Advanced Study (2013).
  16. 16.
    Sørensen, M., Urzyczyin, P.: Lectures on the Curry-Howard Isomorphism. Elsevier Science, Amsterdam (2006)zbMATHGoogle Scholar
  17. 17.
    A Tutorial Introduction to the Lambda Calculus. Accessed 18 Dec 2017
  18. 18.
    Barendregt, H.: Introduction to generalized type systems. J. Funct. Program. 1(2), 125–154 (1991)MathSciNetzbMATHGoogle Scholar
  19. 19.
    The Coq Proof Assistant Reference Manual (v.8.7.0). Accessed 18 Dec 2017
  20. 20.
    Chlipala, A.: Certified Programming with Dependent Types: A Pragmatic Introduction to the Coq Proof Assistant. The MIT Press, Cambridge (2013)zbMATHGoogle Scholar
  21. 21.
    Lytvyn, V.: Pidkhid do pobudovy intelektualnykh system pidtrymky pryiniattia rishen na osnovi ontolohii. Problemy prohramuvannia 4, 43–52 (2013)Google Scholar
  22. 22.
    Ontology Development 101: A Guide to Creating Your First Ontology. Accessed 18 Dec 2017
  23. 23.
    Abiteboul, S., Manolescu, I., Rigaux, P., Rousset, M., Senellart, P.: Web Data Management. Cambridge University Press, New York (2011)CrossRefGoogle Scholar
  24. 24.
    Air travel booking service ontology. Accessed 18 Dec 2017
  25. 25.
    Protégé: a free, open-source ontology editor & framework for building intelligent systems. Accessed 18 Dec 2017
  26. 26.
    DOLCE: A Descriptive Ontology for Linguistic and Cognitive Engineering. Accessed 18 Dec 2017
  27. 27.
    Tayeb, S.H., Noureddine, M.: Measures for the ontological relations in enterprise. Int. J. Mod. Educ. Comput. Sci. 9(9), 13–23 (2017). Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Vasyl Lenko
    • 1
    Email author
  • Volodymyr Pasichnyk
    • 1
  • Natalia Kunanets
    • 1
  • Yuriy Shcherbyna
    • 2
  1. 1.Lviv Polytechnic National UniversityLvivUkraine
  2. 2.Ivan Franko National University of LvivLvivUkraine

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