6.2 Classification Rules 215 cover a solitary example, and removing them would have little effect. Even the remaining nested exception rule covers only two examples. Thus, one can get an excellent feeling for what the rules do by ignoring all the deeper structure and looking only at the first level or two. That is the attraction of rules with exceptions. Discussion All algorithms for producing classification rules that we have described use the basic covering or separate-and-conquer approach. For the simple, noise-free case this produces PRISM (Cendrowska, 1987), an algorithm that is simple and easy to understand. When applied to two-class problems with the closed-world assumption, it is only necessary to produce rules for one class: Then the rules are in disjunctive normal form and can be executed on test instances without any ambiguity arising. When applied to multiclass problems, a separate rule set is produced for each class; thus, a test instance may be assigned to more than one class, or to no class, and further heuristics are necessary if a unique prediction is sought. To reduce overfitting in noisy situations, it is necessary to produce rules that are not "perfect" even on the training set. To do this it is necessary to have a measure