A model of concept formation

Abstract

At first we model the way an intelligence “I” constructs statements from phrases, and then how “I” interlocks these statements to form a string of statements to attain a concept. These strings of statements are called progressions. That is, starting with an initial stimulating relation between two phrases, we study how “I” forms the first statement of the progression and continues from this first statement to form the remaining statements in these progressions to construct a concept. We assume that “I” retains the progressions that it has constructed. Then we show how these retained progressions provide “I” with a platform to incrementally constructs more and more sophisticated conceptual structures. The reason for the construction of these conceptual structures is to achieve additional concepts. Choice plays a very important role in the progression and concept formation. We show that as “I” forms new concepts, it enriches its conceptual structure and makes further concepts attainable. This incremental attainment of concepts is a way in which we humans learn, and this paper studies the attainability of concepts from previously attained concepts. We also study the ability of “I” to apply its progressions and also the ability of “I” to electively manipulate its conceptual structure to achieve new concepts. Application and elective manipulation requires of “I” ingenuity and insight. We also show that as “I” attains new concepts, the conceptual structures change and circumstances arise where unanticipated conceptual discoveries are attainable. As the conceptual structure of “I” is developed, the logical and structural relationships between concepts embedded in this structure also develop. These relationships help “I” understand concepts in the context of other concepts and help “I 1” communicate to another “I 2” information and concept structures. The conceptual structures formed by “I” give rise to a directed web of statement paths which is called a convolution web. The convolution web provides “I” with the paths along which it can reason and obtain new concepts and alternative ways to attain a given concept. This paper is an extension of the ideas introduced in [1]. It is written to be self-contained and the required background is supplied as needed.