Reasons and Filters for Spurious Behaviors

Current methods in qualitative physics (QP) sometimes predict behaviors of physical systems that do not correspond to any real-valued solution . The existence of spurious solutions and their origins have been analyzed for the treatment of differential equations [Kuipers 86], [Schmid 88] as well as of simple equations [Struss 87], [Struss 88a] . For the first case, the reason for the prediction of spurious behaviors is the local nature of the criteria for determining state changes . This paper attempts a continuation and a refinement of this analysis and exploits results from the treatment of differential equations by interval mathematics and the qualitative theory of dynamic systems. The problem is : how can we determine the possible continuations of a qualitative behavior taking into account its complete history? Such global criteria for the elimination of spurious behaviors are developed for 2nd order differential equations.