


Overview
General Formal Ontology (GFO)

9.1 Property Universals and Their Values
At the abstract (universal) level, we distinguish between property
universals and their
values, which include the difference
between phrases like ``the size of a cabinet'' and ``a big cabinet''.
The first phrase refers to a certain aspect of the cabinet. The second phrase
refers to a value of this property of the cabinet,
which reflects a relationship between the property universal, , and
the same property as exhibited by another entity, .
Values of property universals usually appear in
groups which are called value structures
or measurement systems. Each of
these structures corresponds to some property universal. More intuitively, one
could say that the property may be measured with respect to some
measurement system. For instance, sizes may be measured with the
values ``small'', ``big'', or ``very big'', which are the elements of
one value structure. This structure and the particular values of the
sizes of, e.g. a cabinet and a desk, respectively, allow for
comparison of their sizes.
The notion of a value structure
of a property is similar to a quality dimension in
(21)^{22}.
Further, value structures are related to quality spaces in
(39)^{23}. Note, however, that various types of value structures
can be found for the same property. Of course, one is tempted to
include all these value structures within one comprehensive or
``objective'' structure. The latter would cover all values, such that
any other structure appears as a selection of values of the objective
structure. Instead of this, we currently consider it better to have distinct
value structures (e.g. based on some measurement
instrument), which may afterwards be aligned and composed into a
broader structure, than to have a predefined
``objective'' structure. One reason for our approach is that the
precise objective structure is unknown for most properties
(choosing real numbers as isomorphic may often comprise too many
values). In addition, all measurement instruments are restricted to a
certain range of values, which can be measured using this instrument.
Within a value structure, several levels of generality may be
distinguished, but, preliminarily, we understand value structures to be
sets of values. Often it appears that a notion of
distance can be defined, and that certain layers of value structures
are isomorphic to some subset of real numbers, which allows for a
mapping of values to pairs of a real number and a unit, as in the case
of ``10 kg''.
Robert Hoehndorf
20061018

