H.: Alpha galois lattices: an overview

Abstract. What we propose here is to reduce the size of Galois lattices still conserving their formal structure and exhaustivity. For that purpose we use a preliminary partition of the instance set, representing the asso-ciation of a ”type ” to each instance. By redefining the notion of extent of a term in order to cope, to a certain degree (denoted as α), with this partition, we define a particular family of Galois lattices denoted as Al-pha Galois lattices. We discuss the related implication rules defined as inclusion of such α-extents and show that Iceberg (or frequent) concept lattices are Alpha Galois lattices where the partition is reduced to one single class.