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.

Qualitative and Quantitative Knowledge in Classical Mechanics

This thesis investigates what knowledge is necessary to solve mechanics problems. A program NEWTON is described which understands and solves problems in mechanics mini-world of objects moving on surfaces. Facts and equations such as those given in mechanics text need to be represented. However, this is far from sufficient to solve problems. Human problem solvers rely on "common sense" and "qualitative" knowledge which the physics text tacitly assumes to be present. A mechanics problem solver must embody such knowledge. Quantitative knowledge given by equations and more qualitative common sense knowledge are the major research points exposited in this thesis. The major issue in solving problems is planning. Planning involves tentatively outlining a possible path to the solution without actually solving the problem. Such a plan needs to be constructed and debugged in the process of solving the problem. Envisionment, or qualitative simulation of the event, plays a central role in this planning process.