Modus ponens is used in forward inference and backward inference, where the truth of the conclusion is inferred from the truth of the premise. In modus tollens, the falseness of the premise is inferred from the falseness of the conclusion. Although modus ponens is used in general connectionist production systems, modus tollens is rarely used, except in Quinlan’s proposed INFERNO system and in the system proposed by Thornber. A connectionist production system called ConnPS that can perform both modus ponens and modus tollens simultaneously is described. Compared to the INFERNO system, one of the advantages of ConnPS is its supervised learning ability. The rules and examples given as external knowledge are often erroneous and incomplete. In ConnPS, these rules can be refined by using the supervised learning. Both positive and negative examples are presented to ConnPS, onto which the external rules and observations are mapped. Moreover, ConnPS’s implementations of implications, conjunctions, disjunctions and negation are intuitively consistent with Boolean logic.

For machines to perform classification tasks, such as speech and character recognition, appropriately handling deformed patterns is a key to achieving high performance. The authors presents a new type of classification system, an Adaptive Input Field Neu(cid:173) ral Network (AIFNN), which includes a simple pre-trained neural network and an elastic input field attached to an input layer. By using an iterative method, AIFNN can determine an optimal affine translation for an elastic input field to compensate for the original deformations. The convergence of the AIFNN algorithm is shown. AIFNN is applied for handwritten numerals recognition. Conse(cid:173) quently, 10.83% of originally misclassified patterns are correctly categorized and total performance is improved, without modifying the neural network.