Propositional representations have some shortcomings which are solved when using first order logic(FOL). For an in depth introduction to first order logic, see for instance [Tru92, SA91, GGH89, RN95, NM94]. In propositional logic it is difficult to describe cases such as when a person has the same age as shoe-size. A rule for such a case would have to be like:
When using first order logic, one is able to quantify over the domain:
This representation will cover also yet unseen values for the domain, and is therefore clearly preferable. A drawback is the extra complexity the use of FOL adds to the training phase of data mining, since it usually is easier to create a lot of propositional statements, than recognizing them as one FOL-sentence.
A representation form which has been shown to have the same expressive power
as FOL is semantic nets. In a semantic net, the nodes in the graph
denote concepts, and the edges denote relations between the concepts. An
example of a semantic net is given in Figure 
. In the figure,
the human Calvin with yellow hair owns a tiger called Hobbes. Both tigers and
humans are mammals. For a thorough explanation of semantic nets, see
for instance [RN95]. Usually, a semantic net will be easier for a
person to understand than the corresponding logic expression, but a logic
expression could be easier to handle for a computer (although the semantic net
probably will have some similar internal representation.)