Statistical properties of qualitative behaviors
Giorgio Brajnik · 2003
This paper presents a Monte Carlo method for analyzing the space of trajectories entailed by a qualitative differential equation and deriving statistical properties of qualitative behaviors. Estimates of the occurrence probability of behaviors and estimates of parameters defined over numerical trajectories can be computed and used in several ways. For example, behavior probability can be used to rank behaviors and discard those below a significance threshold. Parameter estimation can be used to determine the average maximum response of a controller to a given perturbation. An example of a second--order oscillatory system is discussed. Introduction Formalisms, methods and tools developed by the Qualitative Reasoning community have the potential to represent and deal with levels of uncertainty that are unpaired by those developed within other communities. For example a Qualitative Differential Equation (QDE) and the QSIM simulator (Kuipers, 1994) can represent and deal not only with a s...