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Arbitrary Relations in Formal Concept Analysis and Logical Information Systems

  • Sébastien Ferré
  • Olivier Ridoux
  • Benjamin Sigonneau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3596)

Abstract

A logical view of formal concept analysis considers attributes of a formal context as unary predicates. In a first part, we propose an augmented definition that handles binary relations between objects. A Galois connection is defined on augmented contexts. It represents concept inheritance as usual, but also relations between concepts. As usual, labeling operators are also defined. In particular, concepts and relations are visible and labeled in a single structure. In a second part, we show how relations can be used for navigating in an augmented concept lattice. This part augments the theory of Logical Information Systems. An implementation is sketched, and first experimental results are presented.

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References

  1. 1.
    Godin, R., Missaoui, R., April, A.: Experimental comparison of navigation in a galois lattice with conventional information retrieval methods. International Journal of Man-Machine Studies 38, 747–767 (1993)CrossRefGoogle Scholar
  2. 2.
    Lindig, C.: Concept. In: Köhler, J., Giunchiglia, F., Green, C., Walther, C. (eds.) IJCAI 1995 Workshop on Formal Approaches to the Reuse of Plans, Proofs, and Programs, Montreal, Canada (1995)Google Scholar
  3. 3.
    Ferré, S., Ridoux, O.: A logical generalization of formal concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 371–384. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Ganter, B., Kuznetsov, S.: Formalizing hypotheses with concepts. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 342–356. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Ferré, S., Ridoux, O.: An introduction to logical information systems. Information Processing & Management 40, 383–419 (2004)zbMATHCrossRefGoogle Scholar
  6. 6.
    Wille, R.: Conceptual graphs and formal concept analysis. In: Delugach, H.S., Keeler, M.A., Searle, L., Lukose, D., Sowa, J.F. (eds.) ICCS 1997. LNCS, vol. 1257, pp. 290–303. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Sowa, J.F.: Conceptual structures. Information processing in man and machine. Addison-Wesley, Reading (1984)zbMATHGoogle Scholar
  8. 8.
    Donini, F.M., Lenzerini, M., Nardi, D., Nutt, W.: The complexity of concept languages. Information and Computation 134, 1–58 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Mineau, G., Stumme, G., Wille, R.: Conceptual structures represented by conceptual graphs and formal concept analysis. In: Tepfenhart, W.M., Cyre, W.R. (eds.) ICCS 1999. LNCS, vol. 1640, pp. 423–441. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Prediger, S., Stumme, G.: Theory-driven logical scaling. In: International Workshop on Description Logics, Sweden, vol. 22 (1999)Google Scholar
  11. 11.
    Baader, F., Sertkaya, B.: Applying formal concept analysis to description logics. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 261–286. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Ganter, B., Wille, R.: Formal Concept Analysis — Mathematical Foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  13. 13.
    Padioleau, Y., Ridoux, O.: A logic file system. In: USENIX Annual Technical Conference, General Track, San Antonio, Texas, USA, USENIX, pp. 99–112 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sébastien Ferré
    • 1
  • Olivier Ridoux
    • 1
  • Benjamin Sigonneau
    • 1
  1. 1.IRISA/Université de RennesRennes cedexFrance

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