Qualitative spatial reasoning: The CLOCK project

Abstract

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. (1) We conjecture that no powerful, general-purpose, purely qualitative representation of spatial properties exists (the poverty conjecture). (2) We describe the MD/PV model of spatial reasoning, which overcomes this fundamental limitation by combining the power of diagrams with qualitative spatial representations. In particular, a metric diagram, which combines quantitative and symbolic information, is used as the foundation for constructing a place vocabulary, a symbolic representation of shape and space which supports qualitative spatial reasoning. (3) We claim that shape and connectivity are the central features of qualitative spatial representations for kinematics. We begin by exploring these ideas in detail, pointing out why simpler representations have not proven fruitful. We also describe how inferences can be organized using the MD/PV model. We demonstrate the utility of this model by describing clock, a program which reasons about complex two-dimensional mechanisms. clock starts with a CAD description of a mechanism's parts and constructs a qualitative simulation of how it can behave. clock successfully performed the first complete qualitative simulation of a mechanical clock from first principles, a milestone in qualitative physics. We also examine other work on qualitative spatial reasoning, and show how it fits into this framework. Finally, we discuss new research questions this framework raises.