Knowledge Acquisition under Incomplete Knowledge using Methods from Formal Concept Analysis: Part I

Article type: Research Article

Authors: Holzer, Richard

Affiliations: Department of Mathematics, AG 1, Darmstadt University of Technology, Schloßgartenstr. 7, D-64289 Darmstadt, Germany

Abstract: Formal contexts with unknown entries can be represented by three-valued contexts K=(G, M, {×, o, ?}, I), where a question mark indicates that it is not known whether the object g∈G has the attribute m∈M. To describe logical formulas between columns of such incomplete contexts the Kripke-semantics are used for propositional formulas over the set M of attributes. Attribute implications are considered as special propositional formulas. If a context is too large to be fully represented, an interactive computer algorithm may help the user to get maximal information (with respect to his knowledge) about the valid attribute implications of the unknown context. This computer algorithm is called "attribute exploration".

Keywords: formal concept analysis, incomplete knowledge, attribute exploration

Journal: Fundamenta Informaticae, vol. 63, no. 1, pp. 17-39, 2004