Sound and complete qualitative simulation is impossible

AbstractState-of-the-art qualitative simulators (for instance, QSIM) are known to be sound; no trajectory which is the solution of a concrete equation matching the input can be missing from the output. A simulator which is seen to be incomplete, that is, which produces a spurious prediction for a particular input, can usually be augmented with an additional filter which eliminates that particular class of spurious behaviors, and the question of whether a simulator with purely qualitative input which never predicts spurious behaviors can ever be achieved by adding new filters in this way has remained unanswered until now. We prove that such a sound and complete qualitative simulation algorithm does not exist