An example of a consistent quantitative/qualitative representation of a dynamic system

The author deals with the integration of qualitative and quantitative reasoning methods in the domain of dynamic systems. Typical methods of combining quantitative and qualitative representations using of fuzzy sets and landmark points subdivide the system space into boxes. An example of a representational structure for dynamic systems in which soundness of qualitative reasoning can be assured is shown. The quantitative structure is represented using the notion of a general dynamic system (GDS). The qualitative counterpart is represented by a finite-state automation structure. The two representational substructures are related through functions called qualitative interpretations of dynamic systems. Finding an interpretation function is equivalent to finding an admissible partition of a GDS. An example shows the critical-hypersurface partitioning of the GDS space, given a partitioning of the system´s output. The critical hypersurfaces subdivide the system space into subsets whose shapes, mostly typically, are not boxes