Advertisement

Treating Incomplete Knowledge in Formal Concept Analysis

  • Peter Burmeister
  • Richard Holzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3626)

Abstract

Whenever human knowledge is considered, one has to take into account that such knowledge may be incomplete. Since Formal Concept Analysis (FCA for short) deals with the representation and investigation of such knowledge which can be connected to data tables – in FCA these are represented as formal one- or many-valued contexts –, it seems to be useful to have ways of representing (and dealing with) situations, where one knows about the incompleteness of parts of the represented knowledge. In this note we try to give a survey of what has been done so far in connection with the treatment of incomplete knowledge in FCA. In particular, we shall compare different algorithms developed so far in connection with the knowledge acquisition tool of “attribute exploration”, which also treat incomplete knowledge – cf. in particular [B91], [G99] and [H01]. Moreover, at the end, different treatments of incomplete knowledge in many-valued contexts and databases are discussed.

Keywords

Modal Logic Question Mark Attribute Logic Incomplete Knowledge Formal Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B86/01]
    Burmeister, P.: (assisted by Rust, A., Scheich, P., Newrly, N. Bang, C.). Con- Imp – A program on formal concept analysis of one-valued contexts (running under MS-DOS or Linux resp.). Darmstadt University of Technology (1986/2001)Google Scholar
  2. [B91]
    Burmeister, P.: Merkmalimplikationen bei unvollständigem Wissen. In: Lex, W. (ed.) Proceedings: Arbeitstagung Begriffsanalyse und Künstliche Intelligenz (Clausthal-Zellerfeld 6. - 8. 10. 1988); Technische Universität Clausthal, pp. 15–46 (1991)Google Scholar
  3. [B00]
    Burmeister, P.: ConImp – Ein Programm zur Formalen Begriffsanalyse. In: Stumme, G., Wille, R. (eds.) Begriffliche Wissensverarbeitung: Methoden und Anwendungen, Springer, Heidelberg (2000); See also Formal Concept Analysis with ConImp: Introduction to the Basic Features; (TUD 2003) at http://www.mathematik.tu-darmstadt.de/~burmeister which is more than a translation of the above paperGoogle Scholar
  4. [BH00]
    Burmeister, P., Holzer, R.: On the treatment of incomplete knowledge in Formal Concept Analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 385–398. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. [C79]
    Codd, E.F.: Extending the database relational model to capture more meaning. ACM Transactions on Database Systems 4(4), 397–434 (1979)CrossRefGoogle Scholar
  6. [C86]
    Codd, E.F.: Missing information (applicable and inapplicable) in relational databases. Sigmod 15(4), 53–78 (1986)CrossRefGoogle Scholar
  7. [D86]
    Date, C.J.: Null Values in Database Management, Ch. 15, pp. 313–334. Addison- Wesley, Reading (1986)Google Scholar
  8. [D89]
    Date, C.J.: NOT is not ’Not’ (Notes on three-valued logic and related matters), Ch. 8, pp. 217–248. Addison-Wesley, Reading (1989)Google Scholar
  9. [G99]
    Ganter, B.: Attribute exploration with background knowledge. Theoretical Computer Science 217, 215–233.10 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [G00]
    Ganter, B.: Begriffe und Implikationen. In: Stumme, G., Wille, R. (eds.) Begriffliche Wissensverarbeitung: Methoden und Anwendungen, Springer, Heidelberg (2000)Google Scholar
  11. [GW99]
    Ganter, B., Wille, R.: Formal Concept Analysis – Mathematical Foundations. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  12. [GW00]
    Ganter, B., Wille, R.: Contextual Attribute Logic. In: Töpferhart, W., Cyre, W. (eds.) Conceptual Structures: Standards and Practices, pp. 377–388. Springer, Heidelberg (2000)Google Scholar
  13. [H01]
    Holzer, R.: Methoden der formalen Begriffsanalyse bei der Behandlung unvollständigen Wissens. Dissertation, Shaker Verlag (2001)Google Scholar
  14. [H04]
    Holzer, R.: Knowledge acquisition under incomplete knowledge using methods from formal concept analysis Parts I and II. Fundamenta Informaticae 63(1), 17–39, 41-63 (2004)zbMATHMathSciNetGoogle Scholar
  15. [K97]
    Klein, H.-J.: Gesicherte und mögliche Antworten auf Anfragen an relationale Datenbanken mit partiellen Relationen (1997)Google Scholar
  16. [K98]
    Klein, H.-J.: Model Theoretic and Proof Theoretic View of Relational Databases with Null Values: A Comparison (1998)Google Scholar
  17. [K99]
    Klein, H.-J.: Efficient Algorithms for Approximating Answers to Queries Against Incomplete Relational Databases. In: Proceedings of the 6th International Workshop on Knowledge Representation meets Databases KRDB 1999, Sweden (1999)Google Scholar
  18. [L76]
    Lipski, W.: Informational systems with incomplete information. In: Michaelson, S., Milner, R. (Hrg.) (eds.) Proc. 3rd Int. Symp. on Automata, Languages and Programming (Hrg, Edinburgh, pp. 120–130 (1976)Google Scholar
  19. [L79]
    Lipski, W.: On semantic issues connected with incomplete information databases. ACM Trans. on Database Systems 4(3), 262–296 (1979)CrossRefGoogle Scholar
  20. [L81]
    Lipski, W.: On databases with incomplete information. J. of the ACM 18(1), 41–70 (1981)CrossRefMathSciNetGoogle Scholar
  21. [L84]
    Lipski, W.: On relational algebra with marked nulls. In: Proc. 3rd ACM Symp. on Principles of Database Systems, pp. 201–203 (1984)Google Scholar
  22. [Ma83]
    Maier, D.: The Theory of Relational Databases. Computer Science Press, Rockville (1983)zbMATHGoogle Scholar
  23. [O02]
    Obiedkov, S.: Modal Logic for Evaluating Formulas in Incomplete Contexts. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, pp. 314–325. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  24. [P97]
    Pagliani, P.: Information Gaps as Communication Needs: A New Semantic Foundation for Some Non-Classical Logics. Journal of Logic, Language and Information 6 (1997)Google Scholar
  25. [S95]
    Stumme, G.: Knowledge acquisition by distributive concept exploration. In: Ellis, G., Levinson, R.A., Rich, W., Sowa, J.F. (eds.) Supplementary proceedings of the third international conference on conceptual structures, Santa Cruz, CA, USA, pp. 98–111 (1995)Google Scholar
  26. [S97]
    Stumme, G.: Concept exploration – A tool for creating and exploring conceptual hierarchies. In: Delugach, H.S., Keeler, M.A., Searle, L., Lukose, D., Sowa, J.F. (eds.) ICCS 1997. LNCS, vol. 1257, pp. 318–331. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  27. [W88]
    Wille, R.: Dependencies between many-valued attributes. In: Bock, H.H. (ed.) Classification and Related Methods of Data Analysis (1988)Google Scholar
  28. [W89]
    Wille, R.: Knowledge acquisition by methods of formal concept analysis. In: Diday, E. (ed.) Data analysis, learning symbolic and numeric knowledge, pp. 365–380. Nova Science Publishers, New York (1989)Google Scholar
  29. [Wo93]
    Wolff, K.E.: A first course in formal concept analysis. In: Faulbaum, F. (ed.) SoftStat 1993, Advances in Statistical Software, vol. 4, pp. 429–438 (1993)Google Scholar
  30. [Z91]
    Zickwolff, M.: Rule exploration: first order logic in formal concept analysis. Dissertation, TH Darmstadt (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Peter Burmeister
    • 1
  • Richard Holzer
    • 1
  1. 1.Technische Universität Darmstadt 

Personalised recommendations