A Study of Qualitative and Geometric Knowledge in Reasoning about Motion

Reasoning about motion is an important part of our commonsense knowledge, involving fluent spatial reasoning. This work studies the qualitative and geometric knowledge required to reason in a world that consists of balls moving through space constrained by collisions with surfaces, including dissipative forces and multiple moving objects. An analog geometry representation serves the program as a diagram, allowing many spatial questions to be answered by numeric calculation. It also provides the foundation for the construction and use of place vocabulary, the symbolic descriptions of space required to do qualitative reasoning about motion in the domain. The actual motion of a ball is described as a network consisting of descriptions of qualitatively distinct types of motion. Implementing the elements of these networks in a constraint language allows the same elements to be used for both analysis and simulation of motion. A qualitative description of the actual motion is also used to check the consistency of assumptions about motion. A process of qualitative simulation is used to describe the kinds of motion possible from some state. The ambiguity inherent in such a description can be reduced by assumptions about physical properties of the ball or assumptions about its motion. Each assumption directly rules out some kinds of motion, but other knowledge is required to determine the indirect consequences of making these assumptions. Some of this knowledge is domain dependent and relies heavily on spatial descriptions.

Automatic Design of a Maglev Controller in State Space

We describe the automatic synthesis of a global nonlinear controller for stabilizing a magnetic levitation system. The synthesized control system can stabilize the maglev vehicle with large initial displacements from an equilibrium, and possesses a much larger operating region than the classical linear feedback design for the same system. The controller is automatically synthesized by a suite of computational tools. This work demonstrates that the difficult control synthesis task can be automated, using programs that actively exploit knowledge of nonlinear dynamics and state space and combine powerful numerical and symbolic computations with spatial-reasoning techniques.

Representing and Reasoning About Change in Geologic Interpretation

Geologic interpretation is the task of inferring a sequence of events to explain how a given geologic region could have been formed. This report describes the design and implementation of one part of a geologic interpretation problem solver -- a system which uses a simulation technique called imagining to check the validity of a candidate sequence of events. Imagining uses a combination of qualitative and quantitative simulations to reason about the changes which occured to the geologic region. The spatial changes which occur are simulated by constructing a sequence of diagrams. The quantitative simulation needs numeric parameters which are determined by using the qualitative simulation to establish the cumulative changes to an object and by using a description of the current geologic region to make quantitative measurements. The diversity of reasoning skills used in imagining has necessitated the development of multiple representations, each specialized for a different task. Representations to facilitate doing temporal, spatial and numeric reasoning are described in detail. We have also found it useful to explicitly represent processes. Both the qualitative and quantitative simulations use a discrete 'layer cake' model of geologic processes, but each uses a separate representation, specialized to support the type of simulation. These multiple representations have enabled us to develop a powerful, yet modular, system for reasoning about change.

Qualitative Knowledge, Casual Reasoning and the Localization of Failures

This report investigates some techinques appropriate to representing the knowledge necessary for understanding a class of electronic machines -- radio receivers. A computational performance model - WATSON - is presented. WATSONs task is to isolate failures in radio receivers whose principles of operation have been appropriately described in his knowledge base. The thesis of the report is that hierarchically organized representational structures are essential to the understanding of complex mechanisms. Such structures lead not only to descriptions of machine operation at many levels of detail, but also offer a powerful means of organizing "specialist" knowledge for the repair of machines when they are broken.

Automatic Qualitative Modeling of Dynamic Physical Systems

This report describes MM, a computer program that can model a variety of mechanical and fluid systems. Given a system's structure and qualitative behavior, MM searches for models using an energy-based modeling framework. MM uses general facts about physical systems to relate behavioral and model properties. These facts enable a more focussed search for models than would be obtained by mere comparison of desired and predicted behaviors. When these facts do not apply, MM uses behavior-constrained qualitative simulation to verify candidate models efficiently. MM can also design experiments to distinguish among multiple candidate models.

Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

Image Chunking: Defining Spatial Building Blocks for Scene Analysis

Rapid judgments about the properties and spatial relations of objects are the crux of visually guided interaction with the world. Vision begins, however, with essentially pointwise representations of the scene, such as arrays of pixels or small edge fragments. For adequate time-performance in recognition, manipulation, navigation, and reasoning, the processes that extract meaningful entities from the pointwise representations must exploit parallelism. This report develops a framework for the fast extraction of scene entities, based on a simple, local model of parallel computation.sAn image chunk is a subset of an image that can act as a unit in the course of spatial analysis. A parallel preprocessing stage constructs a variety of simple chunks uniformly over the visual array. On the basis of these chunks, subsequent serial processes locate relevant scene components and assemble detailed descriptions of them rapidly. This thesis defines image chunks that facilitate the most potentially time-consuming operations of spatial analysis---boundary tracing, area coloring, and the selection of locations at which to apply detailed analysis. Fast parallel processes for computing these chunks from images, and chunk-based formulations of indexing, tracing, and coloring, are presented. These processes have been simulated and evaluated on the lisp machine and the connection machine.

Qualitative Process Theory

Objects move, collide, flow, bend, heat up, cool down, stretch, compress and boil. These and other things that cause changes in objects over time are intuitively characterized as processes. To understand common sense physical reasoning and make programs that interact with the physical world as well as people do we must understand qualitative reasoning about processes, when they will occur, their effects, and when they will stop. Qualitative Process theory defines a simple notion of physical process that appears useful as a language in which to write dynamical theories. Reasoning about processes also motivates a new qualitative representation for quantity in terms of inequalities, called quantity space. This report describes the basic concepts of Qualitative Process theory, several different kinds of reasoning that can be performed with them, and discusses its impact on other issues in common sense reasoning about the physical world, such as causal reasoning and measurement interpretation. Several extended examples illustrate the utility of the theory, including figuring out that a boiler can blow up, that an oscillator with friction will eventually stop, and how to say that you can pull with a string but not push with it. This report also describes GIZMO, an implemented computer program which uses Qualitative Process theory to make predictions and interpret simple measurements. The represnetations and algorithms used in GIZMO are described in detail, and illustrated using several examples.

Causal and Teleological Reasoning in Circuit Recognition

This thesis presents a theory of human-like reasoning in the general domain of designed physical systems, and in particular, electronic circuits. One aspect of the theory, causal analysis, describes how the behavior of individual components can be combined to explain the behavior of composite systems. Another aspect of the theory, teleological analysis, describes how the notion that the system has a purpose can be used to aid this causal analysis. The theory is implemented as a computer program, which, given a circuit topology, can construct by qualitative causal analysis a mechanism graph describing the functional topology of the system. This functional topology is then parsed by a grammar for common circuit functions. Ambiguities are introduced into the analysis by the approximate qualitative nature of the analysis. For example, there are often several possible mechanisms which might describe the circuit's function. These are disambiguated by teleological analysis. The requirement that each component be assigned an appropriate purpose in the functional topology imposes a severe constraint which eliminates all the ambiguities. Since both analyses are based on heuristics, the chosen mechanism is a rationalization of how the circuit functions, and does not guarantee that the circuit actually does function. This type of coarse understanding of circuits is useful for analysis, design and troubleshooting.

KAM: Automatic Planning and Interpretation of Numerical Experiments Using Geometrical Methods

KAM is a computer program that can automatically plan, monitor, and interpret numerical experiments with Hamiltonian systems with two degrees of freedom. The program has recently helped solve an open problem in hydrodynamics. Unlike other approaches to qualitative reasoning about physical system dynamics, KAM embodies a significant amount of knowledge about nonlinear dynamics. KAM's ability to control numerical experiments arises from the fact that it not only produces pictures for us to see, but also looks at (sic---in its mind's eye) the pictures it draws to guide its own actions. KAM is organized in three semantic levels: orbit recognition, phase space searching, and parameter space searching. Within each level spatial properties and relationships that are not explicitly represented in the initial representation are extracted by applying three operations ---(1) aggregation, (2) partition, and (3) classification--- iteratively.