GFO Part I Basic Principles
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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, $x$, and the same property as exhibited by another entity, $y$.

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 pre-defined ``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 2006-10-18


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