The Theory of Structured Modeling

Abstract : The author's basic paper An Introduction to Structured Modeling is an informal, example-based exposition. The present paper, in contrast, presents a formal development of the definitions and theory of structured modeling. It is intended for a technical audience rather than for prospective practitioners of the structured modeling approach. The first two sections present the basic definitions of structured modeling. The third develops related theoretical results, and the final section gives a brief conclusion. An extended example illustrating all of the definitions and theoretical properties is given in Appendix I for easy reference. The mathematical prerequisites of this paper are modest. Elementary directed graph theory is the main area requiring some prior familiarity. The terminology used is fairly standard (node, arc, directed cycle, and chain, acyclicity, etc.). Multiple arcs (more than one arc than one arc between a given pair of nodes) are permitted. The term rooted tree means a finite directed graph with no loops, only one node without degree 0, namely the root, and all other nodes without degree 1. The nodes within degree 0 are the terminal nodes. The immediate descendants of any given node are called siblings. (kr)