Summary
J.-P. Doignon and J.-C. Falmagne have introduced a formal notion of knowledge space to develop a scientific approach to the assessment of knowledge. They define a knowledge space as a (finite) set Q of questions together with a collection K, of subsets of Q representing different knowledge states; in addition, they assume that K is closed under set unions. The theory of knowledge spaces can be effectively connected with formal concept analysis. The connection is established by the definition of a knowledge context as a triple (P, Q, I) where P is a finite set of persons, Q is a finite set of questions, and I is a binary relation between P and Q such that plq means: the person p cannot solve the question q. For each knowledge context there is a corresponding knowledge space which consists of the complements of all intents of this context; conversely, each knowledge space can be derived in this way. Via the described connection, methods of formal concept analysis can be successfully applied to the theory of knowledge spaces. In particular, the attribute exploration as a method of conceptual knowledge acquisition yields a new approach for building knowledge spaces.
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References
Burmeister, P. (1995): Conlmp — a program on formal concept analysis of one-valued contexts. Latest version 4.07. TH Darmstadt.
Doignon, J.-P. (1994): Knowledge spaces and skill assignments. In: G.H. Fischer and D. Laming (eds.): Contributions to Mathematical Psychology, Psycho- metrics, and Methodology. Springer-Verlag, New York, 111–121.
Doignon, J.-P., and Falmagne, J.-C. (1985): Spaces for the assessment of knowledge. International Journal of Man-Machine Studies 23, 175–196.
Dowling, C.E. (1993): On the irredundant construction of knowledge spaces. Journal of Mathematical Psychology 37, 49–62.
Duquenne, V., and Guigues, J.-L. (1986): Families minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sri. Humaines 95, 5–18.
Falmagne, J.C., Koppen, M., Villano, M., Doignon, J.-P., and JO- Hannesen, L. (1990): Introduction to knowledge spaces: how to build, test and search them. Psychological Review 97, 201–224.
Ganter, B. (1987): Algorithmen zur Formalen BegrifFsanalyse. In: B. Ganter, R. Wille and K.E. Wolff (eds.): Beiträge zur Begriffsanalyse. B.I.-Wissenschafts-verlag, Mannheim, 241–254.
Ganter, B., and Wille, R. (1986): Implikationen und Abhängigkeiten zwi-schen Merkmalen. In: P.O. Degens, H.-J. Hermes and O. Opitz (eds.): Die Klassifikation und ihr Umfeld. Inders Verlag, Frankfurt, 171–185.
Ganter, B., and Wille, R. (1995): Formale Begriffsanalyse: Mathematische Grundlagen. Springer Verlag, Berlin, Heidelberg (in Vorbereitung).
Kambouri, M., Koppen, M., Villano, M., and Falmagne, J.-C. (1994): Knowledge assessment: tapping human expertise by the QUERY routine. Inter-national Journal of Human-Computer Studies 40, 119–151.
Koppen, M. (1993): Extracting human expertise for constructing knowledge spaces: An algorithm. Journal of Mathematical Psychology 37, 1–20.
Koppen, M., Doignon, J.-P. (1990): How to build a knowledge space by que-rying an expert. Journal of Mathematical Psychology 34, 311–331.
Korossy, K. (1993): Modellierung von Wissen als Kompetenz und Performanz. Dissertation, Universität Heidelberg.
Rusch, A. (1994): Wissensräume und Formale Begriffsanalyse. Diplomarbeit, TH Darmstadt.
Skorsky, M. (1993): ANACONDA - Programm zum Zeichnen von Begriffsver-bänden. TH Darmstadt.
Wild, M. (1991): Implicational bases for finite closure systems. In: W. Lex (ed.): Arbeitstagung Begriffsanalyse und Künstliche Intelligenz. Informatik-Bericht 89/3. TU Clausthal, 147–170.
Wille, R. (1992): Wissensstrukturen und Formale Begriffsanalyse. Vortrag im Psychologischen Kolloquium der Universität Heidelberg.
Wille, R. (1995): Begriffsdenken: Von der griechischen Philosophie bis zur Künstlichen Intelligenz heute. Diltheykastanie, Ludwig-Georgs-Gymnasium Darmstadt, 77–109.
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Rusch, A., Wille, R. (1996). Knowledge Spaces and Formal Concept Analysis. In: Bock, HH., Polasek, W. (eds) Data Analysis and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80098-6_36
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DOI: https://doi.org/10.1007/978-3-642-80098-6_36
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