Implication Structures for System Interconnection Matrices

Abstract

The problem of interconnecting two multilevel subsystem models defined by binary matrices A and B and a common, transitive, contextual relation to form a system model defined by matrix M is solved. The entries of the unknown interconnection matrices X and Y are shown to form a multilevel implication structure. A method for finding this structure is given. The implication matrix that defines the structure furnishes a simple means of determining the inference opportunity of any unknown in X or Y at any point in the development of these matrices. Transitive bordering of A corresponds to the special case B = 1. When the system has many elements, it may be advisable to form a matrix A for a subset and then use transitive bordering iteratively to complete the structuring process.