The Size of a Hyperball in a Conceptual Space
  The cognitive framework of conceptual spaces [3] provides geometric means for
representing knowledge. A conceptual space is a high-dimensional space whose
dimensions are partitioned into so-called domains. Within each domain, the
Euclidean metric is used to compute distances. Distances in the overall space
are computed by applying the Manhattan metric to the intra-domain distances.
Instances are represented as points in this space and concepts are represented
by regions. In this paper, we derive a formula for the size of a hyperball
under the combined metric of a conceptual space. One can think of such a
hyperball as the set of all points having a certain minimal similarity to the
hyperball's center.
