A paradigm example of a concept that is represented in several domains
is “apple” (compare Smith et al. 1988). One of the fi rst problems
when representing a concept is to decide which are the relevant domains.
When we encounter apples as children, the fi rst domains we
learn about are, presumably, those of colour, shape, texture, and taste.
Later, we learn about apples as fruits (biology), about apples as things
with nutritional value, etc.
The next problem is to determine the geometric structure of the domains:
i.e., which are the relevant quality dimensions. Taste space can
be represented by the four dimensions of sweet, sour, salty, and bitter;
the colour domain by hue, saturation, and brightness. Other domains
are trickier. For example, it is diffi cult to say much about the topological
structure of “fruit space”, in part because fruits (such as apples) can
be described relative to several domains. Some ideas about how such
“shape spaces” should be modelled have been discussed in e.g. Marr and
Nishihara (1978), Edelman (1999), and Gärdenfors (2000). Instead of
offering a detailed account of the structures of the different domains, let
me represent the “apple” regions in the domains verbally, as follows: