  We propose a logical analysis of the concept of typicality, central in human
cognition (Rosch,1978). We start from a previously proposed extension of the
basic Description Logic ALC (a computationally tractable fragment of First
Order Logic, used to represent concept inclusions and ontologies) with a
typicality operator T that allows to consistently represent the attribution to
classes of individuals of properties with exceptions (as in the classic example
(i) typical birds fly, (ii) penguins are birds but (iii) typical penguins don't
fly). We then strengthen this extension in order to separately reason about the
typicality with respect to different aspects (e.g., flying, having nice
feather: in the previous example, penguins may not inherit the property of
flying, for which they are exceptional, but can nonetheless inherit other
properties, such as having nice feather).
