Mining (sic) Bases with Adaptable Role Depth

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 has been 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 epsilon(sic)(+/-) 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 epsilon(sic)(+/-) 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 epsilon(sic)(+/-) concept inclusions holding in the interpretation, not only the ones up to a fixed role depth. We also consider the case of confident epsilon(sic)(+/-) 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.