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International Conference on Formal Concept Analysis

ICFCA 2004: Concept Lattices pp 261–286Cite as

Applying Formal Concept Analysis to Description Logics

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2961))

Abstract

Given a finite set \(\mathcal{C} := \{ C_1, \ldots, C_n\}\) of description logic concepts, we are interested in computing the subsumption hierarchy of all least common subsumers of subsets of \(\mathcal{C}\) as well as the hierarchy of all conjunctions of subsets of \(\mathcal{C}\). These hierarchies can be used to support the bottom-up construction of description logic knowledge bases. The point is to compute the first hierarchy without having to compute the least common subsumer for all subsets of \(\mathcal{C}\), and the second hierarchy without having to check all possible pairs of such conjunctions explicitly for subsumption. We will show that methods from formal concept analysis developed for computing concept lattices can be employed for this purpose.

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References

  1. Baader, F.: Computing a minimal representation of the subsumption lattice of all conjunctions of concepts defined in a terminology. In: Ellis, G., Levinson, R.A., Fall, A., Dahl, V. (eds.) Knowledge Retrieval, Use and Storage for Efficiency: Proc. of the 1st Int. KRUSE Symposium, pp. 168–178 (1995)

    Google Scholar 

  2. Baader, F.: Computing the least common subsumer in the description logic EL w.r.t. terminological cycles with descriptive semantics. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS, vol. 2746, pp. 117–130. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Baader, F.: The instance problem and the most specific concept in the description logic EL w.r.t. terminological cycles with descriptive semantics. In: Günter, A., Kruse, R., Neumann, B. (eds.) KI 2003. LNCS (LNAI), vol. 2821, pp. 64–78. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Baader, F.: Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles. In: Gottlob, G., Walsh, T. (eds.) Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 319–324. Morgan Kaufmann, San Francisco (2003)

    Google Scholar 

  5. Baader, F.: Terminological cycles in a description logic with existential restrictions. In: Gottlob, G., Walsh, T. (eds.) Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 325–330. Morgan Kaufmann, San Francisco (2003)

    Google Scholar 

  6. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  7. Baader, F., Franconi, E., Hollunder, B., Nebel, B., Profitlich, H.J.: An empirical analysis of optimization techniques for terminological representation systems or: Making KRIS get a move on. Applied Artificial Intelligence. Special Issue on Knowledge Base Management 4, 109–132 (1994)

    Google Scholar 

  8. Baader, F., Küsters, R.: Computing the least common subsumer and the most specific concept in the presence of cyclic ALN-concept descriptions. In: Herzog, O. (ed.) KI 1998. LNCS, vol. 1504, pp. 129–140. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Baader, F., Küsters, R., Molitor, R.: Computing least common subsumers in description logics with existential restrictions. In: Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI 1999), pp. 96–101 (1999)

    Google Scholar 

  10. Baader, F., Molitor, R.: Building and structuring description logic knowledge bases using least common subsumers and concept analysis. In: Ganter, B., Mineau, G. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 290–303. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  11. Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69, 5–40 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Cohen, W.W., Hirsh, H.: Learning the CLASSIC description logics: Theorethical and experimental results. In: Doyle, J., Sandewall, E., Torasso, P. (eds.) Proc. of the 4th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR 1994), pp. 121–133 (1994)

    Google Scholar 

  13. Dowling, W.F., Gallier, J.H.: Linear-time algorithms for testing the satisfiability of propositional horn formulae. Journal of Logic Programming 1(3), 267–284 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  14. Duquenne, V.: Contextual implications between attributes and some representational properties for finite lattices. In: Ganter, B., Wille, R., Wolf, K.E. (eds.) Beiträge zur Begriffsanalyse, pp. 213–239. B.I. Wissenschaftsverlag, Mannheim (1987)

    Google Scholar 

  15. Frazier, M., Pitt, L.: CLASSIC learning. Machine Learning 25, 151–193 (1996)

    Article  MATH  Google Scholar 

  16. Ganter, B.: Finding all closed sets: A general approach. Order 8, 283–290 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ganter, B.: Attribute exploration with background knowledge. Theoretical Computer Science 217(2), 215–233 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ganter, B., Kuznetsov, S.O.: Pattern structures and their projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129–142. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin (1999)

    MATH  Google Scholar 

  20. Haarslev, V., Möller, R.: High performance reasoning with very large knowledge bases: A practical case study. In: Proc. of the 17th Int. Joint Conf. on Artificial Intelligence, IJCAI 2001 (2001)

    Google Scholar 

  21. Haarslev, V., Möller, R.: RACER system description. In: Proc. of the Int. Joint Conf. on Automated Reasoning, IJCAR 2001 (2001)

    Google Scholar 

  22. Horrocks, I.: Using an expressive description logic: FaCT or fiction. In: Proc. of the 6th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 1998), pp. 636–647 (1998)

    Google Scholar 

  23. Küsters, R., Borgida, A.: What’s in an attribute? Consequences for the least common subsumer. J. of Artificial Intelligence Research 14, 167–203 (2001)

    Google Scholar 

  24. Küsters, R., Molitor, R.: Approximating most specific concepts in description logics with existential restrictions. In: Baader, F., Brewka, G., Eiter, T. (eds.) KI 2001. LNCS (LNAI), vol. 2174, pp. 33–47. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  25. Küsters, R., Molitor, R.: Computing least common subsumers in ALEN. In: Proc. of the 17th Int. Joint Conf. on Artificial Intelligence (IJCAI 2001), pp. 219–224 (2001)

    Google Scholar 

  26. Lutz, C.: Complexity of terminological reasoning revisited. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 181–200. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  27. Marquardt, W.: Trends in computer-aided process modeling. Computers and Chemical Engineering 20(6/7), 591–609 (1996)

    Article  Google Scholar 

  28. Molitor, R.: Unterstützung der Modellierung verfahrenstechnischer Prozesse durch Nicht-Standardinferenzen in Beschreibungslogiken (Supporting the Modelling of of Chemical Processes by Using Non-standard Inferences in Description Logics). PhD thesis, LuFG Theoretical Computer Science, RWTH-Aachen, Germany (2000) (in German)

    Google Scholar 

  29. Nassiri, M.: Berechnung einer erweiterten Subsumtionshierarchie (Computation of an extended subsumption hierarchy). Diploma thesis, RWTH Aachen, Germany (1997) (in German)

    Google Scholar 

  30. Prediger, S.: Terminologische Merkmalslogik in der Formalen Begriffsanalyse. In: [37] (2000)

    Google Scholar 

  31. Prediger, S., Stumme, G.: Theory-driven logical scaling: Conceptual information systems meet description logics. In: Franconi, E., Kifer, M. (eds.) Proc. of the 6th Int. Workshop on Knowledge Representation meets Databases, KRDB 1999 (1999)

    Google Scholar 

  32. Rector, A., Horrocks, I.: Experience building a large, re-usable medical ontology using a description logic with transitivity and concept inclusions. In: Proceedings of the Workshop on Ontological Engineering, AAAI Spring Symposium (AAAI 1997), Stanford, CA, AAAI Press, Menlo Park (1997)

    Google Scholar 

  33. Rudolf, S.: An FCA method for the extensional exploration of relational data. In: Ganter, B., de Moor, A. (eds.) Using Conceptual Structures – Contributions to ICCS 2003, Shaker Verlag, Aachen (2003)

    Google Scholar 

  34. Sattler, U.: Terminological Knowledge Representation Systems in a Process Engineering Application. PhD thesis, LuFG Theoretical Computer Science, RWTH Aachen, Germany (1998)

    Google Scholar 

  35. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48(1), 1–26 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  36. Schultz, S., Hahn, U.: Knowledge engineering by large-scale knowledge reuse—experience from the medical domain. In: Cohn, A.G., Giunchiglia, F., Selman, B. (eds.) Proc. of the 7th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 2000), pp. 601–610. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  37. Stumme, G., Wille, R.: Begriffliche Wissensverarbeitung – Methoden und Anwendungen. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  38. Vogt, F.: Formale Begriffsanalyse mit C++. Springer, Heidelberg (1996)

    Google Scholar 

  39. Zickwolff, M.: Rule Exploration: First Order Logic in Formal Concept Analysis. PhD thesis, TH Darmstadt, Germany (1991)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, D-01062, Dresden, Germany

    Franz Baader & Baris Sertkaya

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  1. Franz Baader
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  2. Baris Sertkaya
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Editors and Affiliations

  1. School of Information Systems and Technology, University of Wollongong, Northfields Ave, NSW 2522, Wollongong, Australia

    Peter Eklund

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© 2004 Springer-Verlag Berlin Heidelberg

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Baader, F., Sertkaya, B. (2004). Applying Formal Concept Analysis to Description Logics. In: Eklund, P. (eds) Concept Lattices. ICFCA 2004. Lecture Notes in Computer Science(), vol 2961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24651-0_24

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  • DOI: https://doi.org/10.1007/978-3-540-24651-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21043-6

  • Online ISBN: 978-3-540-24651-0

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