Qualitative Simulation

Qualitative simulation predicts the set of possible behaviors consistent with a qualitative differential equation model of the world. Its value comes from the ability to express natural types of incomplete knowledge of the world, and the ability to derive a provably complete set of possible behaviors in spite of the incompleteness of the model. A qualitative differential equation model (QDE) is an abstraction of an ordinary differential equation, consisting of a set of real-valued variables and functional, algebraic and differential constraints among them. A QDE model is qualitative in two senses. First, the values of variables are described in terms of their ordinal relations with a finite set of symbolic landmark values, rather than in terms of real numbers. Second, functional relations may be described as monotonic functions (increasing or decreasing over particular ranges) rather than by specifying a functional form. These purely qualitative descriptions can be augmented with semi-quantitative knowledge in the form of real bounding intervals around unknown real values and real-valued bounding envelope functions around unknown real-valued functions. Qualitative and semi-quantitative models can be derived by composing model fragments and collecting the associated modeling assumptions. Qualitative simulation starts with a QDE and a qualitative description of an initial state. Given a qualitative description of a state (called a qstate), it predicts the qualitative state descriptions that can possibly be direct successors of the current state description. Repeating this process produces a graph of qualitative state descriptions, in which the paths starting from the root are the possible qualitative behaviors. The graph of qualitative states is pruned according to criteria derived from the theory of ordinary differential equations, in order to preserve the guarantee that all possible behaviors are predicted. Abstraction methods have also been developed to simplify the resulting qualitative behaviors. The resulting graph of qualitative states (the behavior graph) can still be quite large, requiring automated methods based on temporal logic model-checking to determine whether the qualitative prediction implies a desired conclusion. Conclusions derived in this way can be used in the design and validation of dynamical systems such as controllers. A set of qualitative models and their associated predictions can also be unified with a stream of observations to monitor an ongoing dynamical system or to do system identification on a partial model. Ongoing research topics include qualitative simulation and abstraction methods, the use of various types of quantitative knowledge, automated ways to determine the conclusions to draw from a predicted behavior graph, design and verification methods, online monitoring frameworks, and modeling methods suited for This work has taken place in the Qualitative Reasoning Group at the Artificial Intelligence Laboratory, The University of Texas at Austin. Research of the Qualitative Reasoning Group is supported in part by NSF grants IRI-9504138 and CDA 9617327, by NASA grant NAG 9-898, and by the Texas Advanced Research Program under grants 003658-242 and 003658-347. yComputer Science Department, University of Texas at Austin, Austin, Texas 78712 USA. [email protected].