Generating causal relations from mathematical models

Abstract

System analysis is an important topic for many scientific disciplines. By a system, we mean an orderly, interconnected arrangement of parts describing a phenomenon. The formal representation of systems is done through mathematical modeling. Thus the analysis of a system is performed by analysing the mathematical model of the system. The mathematical model of a system contains implicit information about the system it describes - how the system behaves under various conditions, what are the relationships between the variables, how the cause-effect sequence of the variables be arranged, etc. Currently, the exposition of this information in order to understand the system truly is usually performed by humans. This thesis is a step towards the automation of this process and introduces for this purpose some techniques. These techniques are based on the use of some well-known mathematical tools: partial derivatives and total differentials of the closed form functions defining a system. Partial derivatives and total differentials are analysed to make the causal relations implied by the model explicit. The mathematical models addressed by our work are restricted to models of the form of algebraic equations.