Occasionally it is claimed that neural pattern recognition (or neural network pattern classifcation) should be considered its own discipline, but despite its somewhat di?erent intellectual pedigree, we will consider it a close descendant of statistical pattern recognition, for reasons that will become clear. If instead the model consists of some set of crisp logical rules, then we employ the methods of syntactic pattern recognition, where rules or grammars describe our decision. For example we might wish to classify an English sentence as grammatical or not, and here statistical descriptions (word frequencies, word correlations, etc.) are inapapropriate. 