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.

A System for Representing and Using Real-World Knowledge

This report describes a knowledge-base system in which the information is stored in a network of small parallel processing elements ??de and link units ??ich are controlled by an external serial computer. This network is similar to the semantic network system of Quillian, but is much more tightly controlled. Such a network can perform certain critical deductions and searches very quickly; it avoids many of the problems of current systems, which must use complex heuristics to limit and guided their searches. It is argued (with examples) that the key operation in a knowledge-base system is the intersection of large explicit and semi-explicit sets. The parallel network system does this in a small, essentially constant number of cycles; a serial machine takes time proportional to the size of the sets, except in special cases.

Representing Knowledge of Large-Scale Space

This dissertation presents a model of the knowledge a person has about the spatial structure of a large-scale environment: the "cognitive map". The functions of the cognitive map are to assimilate new information about the environment, to represent the current position, and to answer route-finding and relative-position problems. This model (called the TOUR model) analyzes the cognitive map in terms of symbolic descriptions of the environment and operations on those descriptions. Knowledge about a particular environment is represented in terms of route descriptions, a topological network of paths and places, multiple frames of reference for relative positions, dividing boundaries, and a structure of containing regions. The current position is described by the "You Are Here" pointer, which acts as a working memory and a focus of attention. Operations on the cognitive map are performed by inference rules which act to transfer information among different descriptions and the "You Are Here" pointer. The TOUR model shows how the particular descriptions chosen to represent spatial knowledge support assimilation of new information from local observations into the cognitive map, and how the cognitive map solves route-finding and relative-position problems. A central theme of this research is that the states of partial knowledge supported by a representation are responsible for its ability to function with limited information of computational resources. The representations in the TOUR model provide a rich collection of states of partial knowledge, and therefore exhibit flexible, "common-sense" behavior.