Monotonicity Analysis for Constructing Qualitative Models

Abstract

Qualitative models are more suitable than classical quantitative models in many tasks like Model-based Diagnosis (MBD), explaining system behavior, and designing novel devices from first principles. Monotonicity is an important feature to leverage when constructing qualitative models. Detecting monotone pieces robustly and efficiently from sensor or simulation data remains an open problem. This paper introduces an approach based on scale-dependent monotonicity: the notion that monotonicity can be defined relative to a scale. Real-valued functions defined on a finite set of reals e.g. the sensor data the simulation results, can be partitioned into quasi-monotone segments, i.e. segments monotone with respect to nonzero scale. We can identify the extrema of the quasi-monotone segments. This paper then uses this method to abstract qualitative models from simulation models for the purpose of diagnosis. It shows that using monotone analysis, the abstracted qualitative model is not only sound, but also parsimonious because it generates few landmarks.