Axiomatizing εL⊥-expressible terminological knowledge from erroneous data

In a recent approach, Baader and Distel proposed an algorithm to axiomatize all terminological knowledge that is valid in a given data set and is expressible in the description logic ELK. This approach is based on the mathematical theory of formal concept analysis. However, this algorithm requires the initial data set to be free of errors, an assumption that normally cannot be made for real-world data. In this work, we propose a first extension of the work of Baader and Distel to handle errors in the data set. The approach we present here is based on the notion of confidence, as it has been developed and used in the area of data mining.