In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining ℰℒ⊥ bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining ℰℒ⊥ bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all ℰℒ⊥ concept inclusions holding in the interpretation, not only the ones up to a fixed role depth. We also consider the case of confident ℰℒ⊥ bases, which requires that some proportion of the domain of the interpretation satisfies the base, instead of the whole domain. This case is useful to cope with noisy data.

Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and obtained differ significantly between these two research areas. Despite these differences, there have been several attempts to bridge the gap between these two formalisms, and attempts to apply methods from one field in the other. The present work aims to give an overview on the research done in combining Description Logics and Formal Concept Analysis.