The Role of Classification in Knowledge Representation and Discovery - 1

In summary, hierarchies are excellent representations for knowledge in mature domains in which the nature of the entities, and the nature of meaningful relationships, is known. Hierarchies are useful for entities that are well defined and have clear class boundaries. In general, some theory or model is necessary to guide the identification of entities, the rules of association and distinction, and the order in which these rules are invoked:

Trees. Another type of classificatory structure used to represent entities and their relationships is a tree. A tree divides and subdivides its classes based on specific rules for distinction just as in a hierarchy but does not assume the rules of inheritance. Thus, in a tree, the entities have systematic relationships but not the generic (is-a) relationship. There are many types of relationships that can be represented by a tree (see, for example, Figure 2).

Figure 2. Tree: Chain of Command in the Army

GENERALS
       COLONELS
              CAPTAINS
                     LIEUTENANTS
                            SERGEANTS
                                   PRIVATES

In this tree, the entities are the names of Army ranks. The relationships among the ranks can be described as "chain of command" or "who reports to whom." That is, a GENERAL commands COLONELS, COLONELS report to GENERALS, COLONELS command CAPTAINS, and so on. GENERALS command PRIVATES as well, although not directly, but a PRIVATE is not a kind of SERGEANT, and a SERGEANT is not a kind of LIEUTENANT, SO the principle of division by species/differentia does not apply. Conversely, SERGEANTS do not inherit the attributes of LIEUTENANTS. In terms of knowledge representation, a tree works well to display a particular relationship and the distribution of the entities vis-a-vis that relationship. This tree shows who is on top and who is on the bottom of the chain of command. Some inferences can be made about prerogatives and responsibility, but only weakly since these inferences are based on pragmatic knowledge and not on knowledge that is stored in the structure of the classification itself. By knowing something about the domain, it is also possible to guess that GENERALS once were PRIVATES and thus bring "up the ladder" all of the experiences of going through the ranks, but this is not a formal requirement of the representation either, and may, in fact, be wrong.

Furthermore, a tree is "flatter" in its representation than is a hierarchy; there is less richness in the representation at each level because there is no inheritance or sharing of attributes. For example, there is no indication of the nature of LIEUTENANTS--their essence as it were--from their position in this classification. In a hierarchy, if we know a dog is a mammal, we know something about the mammalian attributes of the entity dog. What are the attributes of a LIEUTENANT that we can learn from the classification? Does a LIEUTENANT share attributes with a GENERAL but has less of them or different kinds? This type of information is not included explicitly. All we can know from this tree is that one rank commands the one lower in the pecking order.