Qualitative Reasoning of a Temporally Hierarchical System Based on Infinitesimal Analysis

In ordinary qualitative reasoning(QR), qualitative behavior of the dynamical systems is predicted by assignment of qualitative values such as {+,0,—} into model variables based on proper transition rules. Unfortunately, due to ambiguities in these ordinarily introduced qualitative values,their arithmetic and transition rules cause predictions to be redundant,sometimes even inaccurate. In this paper,we present a new method of qualitative reasoning which, besides using hyperreal numbers,takes into account their c-H ranking in describing both qualitative values and qualitative derivatives of variables and also employs a convergence filter to investigate the infinitesimal asymptotic behavior of qualitative variables. We applied this qualitative reasoning method to envision a temporally hierarchical complex system.The result shows that this method provides a more detailed and natural qualitative solution than previous methods like Kuipers’s time abstraction in envisioning temporally hierarchical complex system.