CONCEPTUAL TRANSITION FROM LOGIC TO ARITHMETIC IN CONCEPT LEARNING

This paper presents a computational study of the change of the logic-based concepts to arithmeticbased concepts in inductive learning from examples. Specifically, we address the problem of learning concepts whose description in the original knowledge representation space is very complex and difficult to learn using a conventional machine learning approach. By detecting "exclusive-or" patterns in the initially created hypotheses, the system postulates symmetry relations among pairs of initial attributes. The symmetry pairs are then combined into maximal symmetry groups. Each symmetry group leads to a creation of a counting attribute which is added as a new dimension to the representation space. So modified representation space facilitates the determination of new type of concept descriptions, called conditional M-of-N rules. The proposed ideas are illustrated by a visualization method based on the generalized logic diagram (GLD).