  It was recently proved that a sound and complete qualitative simulator does
not exist, that is, as long as the input-output vocabulary of the
state-of-the-art QSIM algorithm is used, there will always be input models
which cause any simulator with a coverage guarantee to make spurious
predictions in its output. In this paper, we examine whether a meaningfully
expressive restriction of this vocabulary is possible so that one can build a
simulator with both the soundness and completeness properties. We prove several
negative results: All sound qualitative simulators, employing subsets of the
QSIM representation which retain the operating region transition feature, and
support at least the addition and constancy constraints, are shown to be
inherently incomplete. Even when the simulations are restricted to run in a
single operating region, a constraint vocabulary containing just the addition,
constancy, derivative, and multiplication relations makes the construction of
sound and complete qualitative simulators impossible.
