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

Article type: Research Article

Authors: Holzer, Richard

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

Abstract: Attribute exploration is an interactive computer algorithm which helps the expert to get informations about the attribute implications of a formal context. In the part I of this paper (see [H04]) an algorithm for attribute exploration with incomplete knowledge was presented. In this part we prove the main results of the algorithm: At the end of the attribute exploration the expert gets maximal information with respect to his knowledge about the unknown universe: He gets a list of implications which are certainly valid, a list of implications which are possibly valid, a list of counterexamples against the implications which are certainly not valid and a list of fictitious counterexamples against the implications which he answered by "unknown". He only has to check the implications which he answered by "unknown" and if he can decide for each of these implications whether it is valid or not, he gets complete knowledge about the implications of the context.

Keywords: formal concept analysis, incomplete knowledge, attribute exploration

Journal: Fundamenta Informaticae, vol. 63, no. 1, pp. 41-63, 2004