Causes of Ineradicable Spurious Predictions in Qualitative Simulation

TL;DR

This paper proves that within the current framework of qualitative simulation, it is impossible to create a sound and complete simulator due to inherent limitations in the input vocabulary and representation features.

Contribution

It demonstrates the fundamental limitations of qualitative simulators using restricted vocabularies, showing that soundness and completeness cannot be achieved simultaneously.

Findings

All sound simulators with certain features are inherently incomplete.

Restricting to a single operating region does not resolve the incompleteness.

Adding basic relations like addition and multiplication still prevents soundness and completeness.

Abstract

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.