Abstract

In the following two sections we propose ordering relations for which the material for comparison of theories of concepts the theories deal with. The relations refer to what is called concept analysis. In the present section we introduce relations enabling us to compare theories from the point of view of the following aspect: How well the theories in question classify objects into positive and negative instances of concepts. Classifications of objects provided by a theory can be correct or incorrect from the point of view of some other theory. The respective relations reflect the following intuition: According to a theory H, a theory H2 is not worse than a theory H1 whenever the set of objects correctly classified by H2 includes that of H1, and the set of objects incorrectly classified by H1 includes that of H2. Let T HR be a family of theories, let CON be a set of concepts, and let OB be a set of objects to which the concepts from CON apply. For A ∈ CON let P) and N) be the sets of objects which satisfy A and do not satisfy A, respectively, according to the classification provided by a theory H ∈ T HR. In other words we consider sets of positive and negative instances of A determined in the respective theories.