Upward refinement operators for conceptual blending in the description logic \(\mathcal {E}\mathcal {L}^{++}\)

  • Roberto ConfalonieriEmail author
  • Manfred Eppe
  • Marco Schorlemmer
  • Oliver Kutz
  • Rafael Peñaloza
  • Enric Plaza


Conceptual blending is a mental process that serves a variety of cognitive purposes, including human creativity. In this line of thinking, human creativity is modeled as a process that takes different mental spaces as input and combines them into a new mental space, called a blend. According to this form of combinational creativity, a blend is constructed by taking the commonalities among the input mental spaces into account, to form a so-called generic space, and by projecting the non-common structure of the input spaces in a selective way to the novel blended space. Since input spaces for interesting blends are often initially incompatible, a generalisation step is needed before they can be blended. In this paper, we apply this idea to blend input spaces specified in the description logic \(\mathcal {E}\mathcal {L}^{++}\) and propose an upward refinement operator for generalising \(\mathcal {E}\mathcal {L}^{++}\) concepts. We show how the generalisation operator is translated to Answer Set Programming (ASP) in order to implement a search process that finds possible generalisations of input concepts. The generalisations obtained by the ASP process are used in a conceptual blending algorithm that generates and evaluates possible combinations of blends. We exemplify our approach in the domain of computer icons.


Computational creativity Conceptual blending Description logic Answer set programming 

Mathematics Subject Classification (2010)

07.05.Mh 89.20.Ff 


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  1. 1.
    Baader, F.: Computing the least common subsumer in the description logic \(\mathcal {E}\mathcal {L}\) w.r.t. terminological cycles with descriptive semantics. In: Ganter, B., De Moor, A., Lex, W. (eds.) Conceptual Structures for Knowledge Creation and Communication, Lecture Notes in Computer Science, vol. 2746, pp 117–130. Springer, Berlin Heidelberg (2003)Google Scholar
  2. 2.
    Baader, F.: A graph-theoretic generalization of the least common subsumer and the most specific concept in the description logic \(\mathcal {E}\mathcal {L}\). In: Hromkovic, J., Nagl, M., Westfechtel, B. (eds.) Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 3353, pp 177–188. Springer, Berlin (2005)Google Scholar
  3. 3.
    Baader, F., Küsters, R: Non-standard inferences in description logics: the story so far. In: Gabbay, D.M., Goncharov, S.S., Zakharyaschev, M. (eds.) Mathematical Problems from Applied Logic I, International Mathematical Series, vol. 4, pp 1–75. Springer, New York (2006)Google Scholar
  4. 4.
    Baader, F., Morawska, B.: Rewriting Techniques and Applications: 20th International Conference, RTA 2009 Brasília, Brazil, 2009 Proceedings. Springer Berlin Heidelberg, Berlin, Heidelberg, chap Unification in the Description Logic EL, pp. 350–364 (2009)Google Scholar
  5. 5.
    Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence, pp 364–369. Morgan Kaufmann Publishers Inc., CA, USA (2005)Google Scholar
  6. 6.
    Baader, F., Sertkaya, B., Turhan, A.Y.: Computing the least common subsumer w.r.t. a background terminology. J. Appl. Log. 5(3), 392–420 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope further. In: Clark, K., Patel-Schneider, P.F. (eds.) Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions (2008)Google Scholar
  8. 8.
    Baral C: Knowledge representation, reasoning and declarative problem solving. Cambridge University Press (2003)Google Scholar
  9. 9.
    Besold TR, Plaza E: Generalize and blend: concept blending based on generalization, analogy, and amalgams. In: Proceedings of the 6th International Conference on Computational Creativity, ICCC15 (2015)Google Scholar
  10. 10.
    Bou, F., Eppe, M., Plaza, E., Schorlemmer, M.: D2.1: Reasoning with amalgams. Technical Report, COINVENT Project, available at (2014)
  11. 11.
    Bou, F., Schorlemmer, M., Corneli, J., Gomez-Ramirez, D., Maclean, E., Smail, A., Pease, A.: The role of blending in mathematical invention. In: Proceedings of the 6th International Conference on Computational Creativity, ICCC15 (2015)Google Scholar
  12. 12.
    Clavel, M., Durán, F, Eker, S., Lincoln, P., Martí-Oliet, N, Meseguer, J., Talcott, C.: The Maude 2.0 System. In: Nieuwenhuis, R. (ed.) Rewriting Techniques and Applications (RTA 2003), pp 76–87. Springer-Verlag, no. 2706 in Lecture Notes in Computer Science (2003)Google Scholar
  13. 13.
    Confalonieri, R., Nieves, J.C.: Nested preferences in answer set programming. Fundamenta Informaticae 113(1), 19–39 (2011)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Confalonieri, R., Prade, H.: Using possibilistic logic for modeling qualitative decision: answer set programming algorithms. Int. J. Approximate Reasoning 55(2), 711–738 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Confalonieri, R., Corneli, J., Pease, A., Plaza, E., Schorlemmer, M.: Using argumentation to evaluate concept blends in combinatorial creativity. In: Proceedings of the 6th International Conference on Computational Creativity, ICCC15 (2015a)Google Scholar
  16. 16.
    Confalonieri, R., Eppe, M., Schorlemmer, M., Kutz, O., Peñaloza, R, Plaza, E.: Upward refinement for conceptual blending in description logic —an ASP-based approach and case study in \(\mathcal {E}\mathcal {L}^{++}\). In: Proceedings of 1st International workshop of Ontologies and Logic Programming for Query Answering, ONTOLP 2015, co-located with IJCAI-2015 (2015b)Google Scholar
  17. 17.
    Cornet, R., De Keizer, N.: Forty years of SNOMED: a literature review. BMC Med. Inf. Decis. Making 8(Suppl 1) (2008)Google Scholar
  18. 18.
    Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. Artif. Intell. 172(12–13), 1495–1539 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Eppe, M., Bhatt, M.: Narrative based postdictive reasoning for cognitive robotics. In: International Symposium on Logical Formalizations of Commonsense Reasoning (CR) (2013)Google Scholar
  20. 20.
    Eppe, M., Bhatt, M.: Approximate postdictive reasoning with answer set programming. J. Appl. Log. 13(4, Part 3), 676–719 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Eppe, M., Bhatt, M., Dylla, F.: Approximate epistemic planning with postdiction as answer-set programming. In: Cabalar, P., Son, T.C. (eds.) Proceedings of the 12th International Conference Logic Programming and Nonmonotonic Reasoning, LPNMR 2013, Corunna, Spain, pp 290–303. Springer, Berlin (2013)Google Scholar
  22. 22.
    Eppe, M., Bhatt, M., Suchan, J., Tietzen, B.: ExpCog: experiments in commonsense cognitive robotics. In: International Workshop on Cognitive Robotics (CogRob) (2014)Google Scholar
  23. 23.
    Eppe, M., Confalonieri, R., Maclean, E., Kaliakatsos-Papakostas, M.A., Cambouropoulos, E., Schorlemmer, W.M., Codescu, M., Kühnberger, K: Computational invention of cadences and chord progressions by conceptual chord-blending. In: Yang, Q., Wooldridge, M. (eds.) Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, pp 2445–2451. AAAI Press, Buenos Aires, Argentina (2015a)Google Scholar
  24. 24.
    Eppe, M., Maclean, E., Confalonieri, R., Kutz, O., Schorlemmer, W.M., Plaza, E.: ASP, amalgamation, and the conceptual blending workflow. In: Calimeri, F., Ianni, G., Truszczynski, M. (eds.) Logic Programming and Nonmonotonic Reasoning - 13th International Conference, LPNMR 2015, pp 309–316. Proceedings, KY, USA (2015b)Google Scholar
  25. 25.
    Fauconnier, G., Turner, M.: The Way we Think: Conceptual Blending and the Mind’s Hidden Complexities. Basic Books (2002)Google Scholar
  26. 26.
    Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Clingo = ASP + control: Preliminary report. CoRR arXiv:1405.3694 (2014)
  27. 27.
    Gebser, M., Kaminski, R., Kaufmann, B., Lindauer, M., Ostrowski, M., Romero, J., Schaub, T., Thiele, S.: Potassco User Guide 2.0. Technical Report, University of Potsdam (2015)Google Scholar
  28. 28.
    Gelfond, M., Kahl, Y.: Knowledge representation, reasoning, and the design of intelligent agents: the answer-set programming approach. Cambridge University Press, New York (2014)CrossRefGoogle Scholar
  29. 29.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of the Fifth International Conference on Logic Programming, (ICLP’88), pp 1070–1080. The MIT Press (1988)Google Scholar
  30. 30.
    Hois, J., Kutz, O., Mossakowski, T., Bateman, J.: Towards ontological blending. In: Dicheva, D., Dochev, D. (eds.) Artificial Intelligence: Methodology, Systems, and Applications, Lecture Notes in Computer Science, vol. 6304, pp 263–264. Springer, Berlin (2010)Google Scholar
  31. 31.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible SROIQ. In: Doherty, P., Mylopoulos, J., Welty, C.A. (eds.) Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, Lake District of the United Kingdom, pp 57–67. AAAI Press (2006)Google Scholar
  32. 32.
    Kowalski, R.: Predicate logic as programming language. In: Proceedings of International Federation for Information Processing, pp 569–574 (1974)Google Scholar
  33. 33.
    Kutz, O., Bateman, J., Neuhaus, F., Mossakowski, T., Bhatt, M.: E pluribus unum: Formalisation, use-cases, and computational support for conceptual blending. In: Computational Creativity Research: Towards Creative Machines, Thinking Machines, Atlantis/Springer (2014)Google Scholar
  34. 34.
    Lee, J., Palla, R.: Reformulating the situation calculus and the event calculus in the general theory of stable models and in answer set programming. J. Artif. Intell. Res. 43, 571–620 (2012)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Lehmann, J., Haase, C.: Ideal Downward Refinement in the EL Description Logic. In: Proceedings of the 19th International Conference on Inductive Logic Programming, vol. ILP’09, pp 73–87. Springer, Berlin (2010)Google Scholar
  36. 36.
    Lehmann, J., Hitzler, P.: Concept learning in description logics using refinement operators. Mach. Learn. 78(1-2), 203–250 (2010)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Ma, J., Miller, R., Morgenstern, L., Patkos, T.: An epistemic event calculus for ASP-based reasoning about knowledge of the past, present and future. In: International Conference on Logic for Programming, Artificial Intelligence and Reasoning (2013)Google Scholar
  38. 38.
    McCarthy, J.: Applications of circumscription to forMalizing common-sense knowledge. Artif. Intell. 28(1), 89–116 (1986)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Mendez, J.: jcel: A modular rule-based reasoner. In: proceedings of the 1st International Workshop on OWL Reasoner Evaluation (ORE), p 858 (2012)Google Scholar
  40. 40.
    Ontañón, S, Plaza, E.: Amalgams: A Formal Approach for Combining Multiple Case Solutions. In: Bichindaritz, I., Montani, S. (eds.) Proceedings of the International Conference on Case Base Reasoning, Springer, Lecture Notes in Computer Science, vol. 6176, pp 257–271 (2010)Google Scholar
  41. 41.
    Ontañón, S, Plaza, E.: Similarity measures over refinement graphs. Mach. Learn. J. 87(1), 57–92 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Ricca, F., Gallucci, L., Schindlauer, R., Dell’Armi, T., Grasso, G., Leone, N.: OntoDLV: An ASP-based system for enterprise ontologies. J. Log. Comput. 19 (4), 643–670 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Sánchez-Ruiz, A, Ontañón, S, González-Calero, P, Plaza, E.: Refinement-based similarity measure over DL conjunctive queries. In: Delany, S., Ontañón, S. (eds.) Case-Based Reasoning Research and Development, Lecture Notes in Computer Science, vol. 7969, pp 270–284. Springer, Berlin (2013)Google Scholar
  44. 44.
    Spackman, K., Campbell, K., Cote, R.: SNOMED RT: A reference terminology for health care. Journal of the American Medical Informatics Association (1997)Google Scholar
  45. 45.
    Swift, T.: Deduction in Ontologies via ASP. In: Lifschitz, V., Niemelä, I. (eds.) Logic Programming and Nonmonotonic Reasoning, Lecture Notes in Computer Science, vol. 2923, pp 275–288. Springer, Berlin (2004)Google Scholar
  46. 46.
    Toivonen, H., Gross, O.: Data mining and machine learning in computational creativity. Wiley Interdisc. Rev. Data Min. Knowl. Discov. 5(6), 265–275 (2015)CrossRefGoogle Scholar
  47. 47.
    Turhan, A., Zarrieß, B: Computing the lcs w.r.t. general \(\mathcal {E}\mathcal {L}^{+}\)-TBoxes. In: Proceedings of the 26th International Workshop on Description Logics, pp 477–488 (2013)Google Scholar
  48. 48.
    van der Laag, P.R., Nienhuys-Cheng, S.H.: Completeness and properness of refinement operators in inductive logic programming. J. Log. Programm. 34(3), 201–225 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Zarrieß, B, Turhan, A.Y.: Most specific generalizations w.r.t. general \(\mathcal {E}\mathcal {L}\)-TBoxes. In: Proceedings of the 23th International Joint Conference on Artificial Intelligence, AAAI Press, IJCAI’13, pp 1191–1197 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Artificial Intelligence Research Institute (IIIA-CSIC)Campus Universitat Autònoma BarcelonaBellaterraSpain
  2. 2.International Computer Science InstituteBerkeleyUSA
  3. 3.Research Centre for Knowledge and Data (KRDB)Free University of Bozen-BolzanoBozen-BolzanoItaly

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