A Qualitative System Theory : Introducing Global View into Qualitative Reasoning

Many of the qualitative simulation algorithms so far proposed depend upon local propagation paradigm, and hence produce spurious states . Recent approaches use topological constraints in phase space diagrams for filtering the spurious states . We propose an alternative method of recognizing global properties in the graphically expressed qualitative model. Qualitative versions of such system-theoretic concepts as stability and observability are used to analyze the global properties of the system . We first present structural conditions for recognizing qualitative stability or instability in the qualitative model. Then, we generalize several qualitative properties such as .sign/ potential stability, sign observability, potential periodicity constant, invariant sign patterns, using the concept of inertia . These qualitative properties with respect to interia can then be associated with the structure of graphically expressed dynamic. systems . A principle of reasoning about the qualitative properties based on structural changes of graphs is also presented, and used for qualitative reasoning at the structural level .