There are other representations which differ conceptually from propositional statements and first order logic. One of these is the neural net which is much mentioned in literature and used within data mining.
A neural network (see [AM95, RN95] for an introduction) consists of many simple computational elements connected together. One such element, called a neuron, takes as input several values from its neighboring neurons. The weighed sum of these inputs are calculated, and a output value is computed from this. The function calculating the output value is called an activation function, and is normally common for all the neurons.
When being used for classification, some of the neurons are connected to the condition attribute values, and a classification is given from some of the other neurons' outputs. During the learning phase, the attributes of the training set are sent to the inputs, and the output of the net is is compared to the desired one. In case of a mismatch, the weights of the neurons are adjusted in order to classify better later on. After a while, the weights of such a net will usually converge. It should be noted, that as a result of this approach, there is no clear distinction between the learned knowledge and the learning itself in a neural net. A neural net could thus be regarded as a way of inferring information, a way of representing knowledge, or perhaps rather as both.