Axiomatizing Qualitative Process Theory

We show that the type of reasoning performed by Forbus' 1985] Qualitative Process (QP) program can be justiied in a rst-order theory that models time and other measure spaces as real-valued quantities. We consider the QP analysis of a can of water with a safety valve being heated over a ame. We exhibit a rst-order theory for the microworld involved in this example, and we prove the correctness of the rst two transitions in the envisionment graph. We discuss the possibility of deriving the closure conditions in the theory via non-monotonic inference. One way to increase conndence in a reasoning program is to show that the conclusions that it draws correspond to valid inferences within some easily intelligible logical theory. Such a correspondence has been shown for many of the best known physical reasoning programs. The calculations performed by QSIM Kuipers, 86] correspond to theorems in real analysis, under a natural interpretation ; Duchier, 91] exhibits full rst-order proofs of these. Likewise the reasoning in NEWTON de Kleer, 77] and ENVISION de Kleer and Brown, 85] can be shown to be valid for a simple physical theory, easily formalized in rst-order logic, in which time and other physical parameters are viewed as real-valued quantities. (See, for example, Rayner, 91], Davis, 90, chap. 7].) However, no adequate logical analysis has hitherto been given for the Qualitative Process (QP) program Forbus, 85]. In QP, processes can come into and out of existence, and the topological structure of the physical system may change over time. Hence, the problem of nding an appropriate formulation of the necessary closed-world assumptions on processes and innuences seemed daunting. In a previous analysis Davis, 90] I was unable to nd a reasonable characterization of these closure principles, and hence left them as intuitively plausible, but wholly unformalized, non-monotonic deductions. In this paper, I show that this gap can be closed. It is possible to characterize inference in QP entirely in terms of a monotonic theory based on real analysis. There are two key points: For each parameter, the theory must give an exhaustive enumeration of the types of processes and parameters that can innuence it. These axioms resemble to the kind of frame axioms advocated by Schubert 1991], which give necessary conditions for a uent to change its value. They are also analogous to the circumscription over causes of change discussed in Lifschitz, 87]. Since QP uses only …