Improved Reasoning About Infinity Using Qualitative Simulation

Abstract

The AI technique of qualitative simulation, enabling the representation and use of incomplete knowledge, is a useful mathematical tool, especially for the analysis, design, and diagnosis of dynamic systems. One desirable property of qualitative simulators is their ability to handle infinite ``values'' explicitly, leading to formal predictions about asymptotic behavior. We present two modifications to the qualitative simulation algorithm QSIM, which improve the technique's performance in reasoning tasks involving infinite values and infinite time. The first modification corrects an error which causes the algorithm to miss certain real solutions of the simulated equation. The second modification augments the temporal attribute computation routine, and results in better identification of infinite time intervals by the algorithm. This, in turn, helps our modified algorithm to successfully eliminate some additional inconsistent predictions from its output set. We show that several famous qualitative physics problems are handled with increased predictive accuracy by the new algorithm.