Relations and GUHA-Style Data Mining II

  • Petr Hájek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)


The problem of representability of a (finite) Boolean algebra with an additional binary relation by a data matrix (information structure) and a binary generalized quantifier is studied for various classes of (associational) quantifiers. The computational complexity of the problem for the class of all associational quantifiers and for the class of all implicational quantifiers is determined and the problem is related to (generalized) threshold functions and (positive) assumability.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Düntsch, I., Orłowska, E.: Beyond modalities: Sufficiency and mixed algebras. In: Orlowska, et al. (eds.) Relational methods for computer science applications, pp. 263–286. Physica Verlag, Heidelberg (2001)Google Scholar
  2. 2.
    Hájek, P., Havel, I., Chytil, M.: The GUHA method of automatic hypotheses determination. Computing 1, 293–308 (1966)zbMATHCrossRefGoogle Scholar
  3. 3.
    Hájek, P., Havránek, T.: Mechanizing Hypothesis Formation (Mathematical Foundations for a General Theory), p. 396. Springer, Heidelberg (1978), Free internet version: zbMATHGoogle Scholar
  4. 4.
    Hájek, P., Sochorová, A., Zvárová, J.: GUHA for personal computers. Comp. Stat., Data Arch. 19, 149–153Google Scholar
  5. 5.
    Hájek, P.: Relations in GUHA style data mining. In: Proc. Relmics 6, Tilburg, The Netherlands, pp. 91–96Google Scholar
  6. 6.
    Hájek, P.: The GUHA method and mining association rules. In: Proc. CIMA 2001, Bangor, Wales, pp. 533–539 (2001)Google Scholar
  7. 7.
    Hájek, P., Holeňa, M.: Formal logics of discovery and hypothesis formation by machine. Theoretical Computer 292, 345–357 (2003)zbMATHCrossRefGoogle Scholar
  8. 8.
    Hájek, P.: On generalized quantifiers, finite sets and data mining. In: Klopotek, et al. (eds.) Intelligent Information Processing and Data Mining, pp. 489–496. Physica Verlag, Heidelberg (2003)Google Scholar
  9. 9.
    Muroga, S.: Threshold logic and its applications. Wiley, Chichester (1971)zbMATHGoogle Scholar
  10. 10.
    Rauch, J., Šimůnek, M.: Mining for 4ft association rules. In: Morishita, S., Arikawa, S. (eds.) DS 2000. LNCS (LNAI), vol. 1967, pp. 268–272. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Rauch, J.: Interesting Association Rules and Multi-relational Association Rules. Communications of Institute of Information and Computing Machinery 5(2), 77–82 (2002)MathSciNetGoogle Scholar
  12. 12.
    Servedio, R.A.: Probabilistic construction of monotone formulae for positive linear threshold functions (1999) unpublished manuscript from see
  13. 13.
    GUHA+– project web site,
  14. 14.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Petr Hájek
    • 1
  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPrague 8Czech Republic

Personalised recommendations