Pink panthers and toothless tigers: Three problems in classification

Many aspects of how humans form and combine concepts are notoriously difficult to capture formally. In this paper, we focus on the representation of three particular such aspects, namely overextension, underextension, and dominance. Inspired in part by the work of Hampton, we consider concepts as given through a prototype view, and by considering the interdependencies between the attributes that define a concept. To approach this formally, we employ a recently introduced family of operators that enrich Description Logic languages. These operators aim to characterise complex concepts by collecting those instances that apply, in a finely controlled way, to `enough' of the concept's defining attributes. Here, the meaning of `enough' is technically realised by accumulating weights of satisfied attributes and comparing with a given threshold that needs to be met.