Artificial Intelligence 51, pp. 95-143

Artificial Intelligence 51 (1991) 417-471, Spatial reasoning is ubiquitous in human problem solving. Significantly, many aspects of it appear to be qualitative. This paper describes a general framework for qualitative spatial reasoning and demonstrates how it can be used to understand complex mechanical systems, such as clocks. The framework is organized around three ideas.

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A qualitative physics which captures the depth and breadth of an engineer's knowledge will be orders of magnitude larger than the models of today's qualitative physics. To build and use such models effectively requires explicit modeIing assumptions to manage complexity. This, in turn, gives rise to the problem of selecting the right qualitative model for some purpose.

This volume brings together current work on qualitative reasoning. Previous publication has been primarily in scattered conference proceedings. The appearance of this volume reflects the maturity of qualitative reasoning as a research area, and the growing interest in problems of reasoning about physical systems. Anyone concerned with automated reasoning about the real (physical) world should read and understand this material.

ABSTRACT: Objects move, collide, flow, bend, heat up, cool down, stretch, compress . and boil. These and otherthings that cause changes in objects over time are intuitively characterized as processes . To understandcommonsense physical reasoning and make programs that interact with the physical world as well aspeople do we must understand qualitative reasoning about processes, when they will occur, theireffects, and when they will stop. Qualitative process theory defines a simple notion of physical processthat appears useful as a language in which to write dynamical theories. Reasoning about processesalso motivates a new qualitative representation for quantity in terms of inequalities, called thequantity space . This paper describes the basic concepts of qualitative process theory, several differentkinds of reasoning that can be performed with them, and discusses its implications for causalreasoning. Several extended examples illustrate the utility of the theory, including figuring out that aboiler can blow up, that an oscillator with friction will eventually stop, and how to say that you canpull with a string, but not push with it. Journal-length version of Ph.D. dissertation, , MIT, 1985.Artifiicial Intelligence. Also In Bobrow, D. (Ed.), Qualitative Reasoning About Physical Systems, pp. 85–186. MIT Press. Also in Artificial Intelligence 24:85-168 (1984).

The spatial and qualitative aspects of reasoning about motion through fret space arc studied through the construction of a program to perform such reasoning. An analog gcomctry rcprcscntation serves as a diagram, and descriptions of both the actual motion of a ball and envisioning are used in answering simple questions. WC ignore the exact shape of balls, motion after two balls collide, spin, motion in a third spatial dimension, air resistance, sliding motion, and all forces other than gravity. The initial description of a situation is a diagram containing a description of the surfaces and one or more bails, as in ligure 1. 1 Introduction People reason fluently about motion through space. For example, WC know that if two balls arc thrown into a well they might collide, but if one ball is always outside and the other always inside they cannot. The knowl"cdgc involved in this qualitative kind of reasoning seems to be simpler than formal mechanics and appears to be based on our expcricnce in the physical world.