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.
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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)
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)
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 paper
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)
Codd, E.F.: Extending the database relational model to capture more meaning. ACM Transactions on Database Systems 4(4), 397–434 (1979)
Codd, E.F.: Missing information (applicable and inapplicable) in relational databases. Sigmod 15(4), 53–78 (1986)
Date, C.J.: Null Values in Database Management, Ch. 15, pp. 313–334. Addison- Wesley, Reading (1986)
Date, C.J.: NOT is not ’Not’ (Notes on three-valued logic and related matters), Ch. 8, pp. 217–248. Addison-Wesley, Reading (1989)
Ganter, B.: Attribute exploration with background knowledge. Theoretical Computer Science 217, 215–233.10 (1999)
Ganter, B.: Begriffe und Implikationen. In: Stumme, G., Wille, R. (eds.) Begriffliche Wissensverarbeitung: Methoden und Anwendungen, Springer, Heidelberg (2000)
Ganter, B., Wille, R.: Formal Concept Analysis – Mathematical Foundations. Springer, Heidelberg (1999)
Ganter, B., Wille, R.: Contextual Attribute Logic. In: Töpferhart, W., Cyre, W. (eds.) Conceptual Structures: Standards and Practices, pp. 377–388. Springer, Heidelberg (2000)
Holzer, R.: Methoden der formalen Begriffsanalyse bei der Behandlung unvollständigen Wissens. Dissertation, Shaker Verlag (2001)
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)
Klein, H.-J.: Gesicherte und mögliche Antworten auf Anfragen an relationale Datenbanken mit partiellen Relationen (1997)
Klein, H.-J.: Model Theoretic and Proof Theoretic View of Relational Databases with Null Values: A Comparison (1998)
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)
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)
Lipski, W.: On semantic issues connected with incomplete information databases. ACM Trans. on Database Systems 4(3), 262–296 (1979)
Lipski, W.: On databases with incomplete information. J. of the ACM 18(1), 41–70 (1981)
Lipski, W.: On relational algebra with marked nulls. In: Proc. 3rd ACM Symp. on Principles of Database Systems, pp. 201–203 (1984)
Maier, D.: The Theory of Relational Databases. Computer Science Press, Rockville (1983)
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)
Pagliani, P.: Information Gaps as Communication Needs: A New Semantic Foundation for Some Non-Classical Logics. Journal of Logic, Language and Information 6 (1997)
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)
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)
Wille, R.: Dependencies between many-valued attributes. In: Bock, H.H. (ed.) Classification and Related Methods of Data Analysis (1988)
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)
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)
Zickwolff, M.: Rule exploration: first order logic in formal concept analysis. Dissertation, TH Darmstadt (1991)
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Burmeister, P., Holzer, R. (2005). Treating Incomplete Knowledge in Formal Concept Analysis. In: Ganter, B., Stumme, G., Wille, R. (eds) Formal Concept Analysis. Lecture Notes in Computer Science(), vol 3626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11528784_6
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