On the Usability of Probably Approximately Correct Implication Bases

Abstract: We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use-cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide qualitative insight that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.