Qualitative Reasoning With Higher-Order Derivatives

Book One

Volume

Proceedings of the AAAI Conference on Artificial Intelligence, 4

Automated Reasoning

The goals of qualitative physics are to identify the distinctions and laws which govern qualitative behavior of devices such that it is possible to predict and explain the behavior of physical devices without recourse to quantitative methods. Although qualitative analysis lacks quantitative information, it predicts significant characteristics of device functioning such as feedback, ringing oscillation, etc. This paper defines higher-order qualitative derivatives and uses them to formulate six fundamental laws which govern the gross-time behavior of physical devices. These qualitative laws are based on the Mean Value Theorem and Taylor’s Expansion of the quantitative calculus. They substitute for what often requires sophisticated problem-solving. We claim they are the best that can be achieved relying on qualitative information.