Abstraction, taxonomies, connectivity: from AI to FCA and back

Abstract. We describe an experience of transfer and ideas exchange between AI and FCA. The original motivation was a data analysis problem in which there were objects, structured attributes together with a categorization of objects, lead-ing to the idea that in some way the categorization should alter the selection of interesting patterns. On one hand, soon it appeared that to investigate the data it was interesting to use various degrees of coarseness not only on the pattern language but also on the extensions, i.e. the support, following the data mining terminology, of the patterns. On an other hand, closed patterns are known to sum-marize the whole set of frequent patterns, and FCA proposes to organize these closed patterns into a concept lattice, each node of which was a pair made of a closed pattern and its extension, but there were no known way to use categoriza-tion and relative coarseness in a flexible way. On the FCA technical side, this led us in particular to extend concept lattices to smaller conceptual structures, called abstract concept lattices, in which the extension of a term/motif/pattern in a set of objects is constrained by an external a priori view of the data together with