4. Properties and concepts
Conceptual spaces theory will next be used to defi ne a property. The
following criterion was proposed in Gärdenfors (1990, 2000), where the
geometrical characteristics of the quality dimensions are used to introduce
a spatial structure to properties:
Criterion P: A property is a convex region in some domain.
The motivation for criterion P is that, if some objects located at x
and y in relation to some quality dimension(s) are both examples of a
concept, then any object that is located between x and y with respect to
the same quality dimension(s) will also be an example of the concept.
This is the defi nition of convexity.
Properties, as defi ned by criterion P, form a special case of concepts.
I defi ne this distinction in Gärdenfors (2000) by saying that a property
is based on a single domain, while a concept is based on one or more
domains. This distinction has been obliterated in both symbolic and
connectionist accounts, which have dominated the discussions in cognitive
science. For example, both properties and concepts are represented
by predicates in fi rst-order logic. However, the predicates of fi rst-order
logic correspond to several different word classes in natural language,
most importantly those of adjectives, nouns, and verbs.