Order Of Magnitude Reasoning

Abstract

This paper presents a methodology for extending representation and reasoning in Qualitative Physics. This methodology is presently used for various applications. The qualitative modeling of a physical system is weakened by the lack of quantitative information. This may lead a qualitative analysis to ambiguity. One of the aims of this methodology is to cope with the lack of quantitative information. The main idea is to reproduce the physicist’s ability to evaluate the influence of different phenomena according to their relative order of magnitude and to use this information to distinguish among radically different ways in which a physical system may behave. A formal system, FOG, is described in order to represent and structure this kind of apparently vague and intuitive knowledge so that it can be used for qualitative reasoning. The validity of FOG for an interpretation in a mathematical theory called Non-Standard Analysis is then proven. Last, it is shown how FOG structures the quantity-space.