Qualitative Spatial Reasoning: Framework and Frontiers

Abstract

Spatial reasoning is a diverse topic; what might different spatial tasks have in common? One task where substantial progress has been made is qualitative spatial reasoning about motion. Unlike qualitative dynamics, purely qualitative spatial representations have not prove n fruitful. Instead, a diagrammatic representation appears to be necessary. This paper begins by outlining the Metric Diagram/Place Vocab. ulary (MD/PV) model of qualitative spatial reasoning, illustrating its power with via two example systems-~FZ0B, a system which reasoned about motion, and CLOCK, a system which analysed fixed-axis mechanisms. We believe this model is applicable beyond simply reasoning about motion. We suspect that (1) some form of metric diagram is a central unifying factor in all spatial reasoning tasks and (2) for human spatial reasoning, the metric diagram is part of, or at least grounded in, our perceptual apparatus. In this spirit, we identify three other kinds of spatial reasoning tasks as research frontiers where substantial progress might also be made, and pose six challenge problems to serve as milestones. The frontiers are (I) deriving system function from concrete structural descriptions (2) representing and reasoning about spatially distributed systems and (3) explicating the role visual perception and recognition in reasoning.

Dynamic Imagery: A Computational Model of Motion and Visual Analogy

“…He did not, however, attempt to represent the organization of scenes or the motions of objects. Forbus (1995) Tabachnik-Schijf, Leonardo, and Simon (1997) proposed the CaMeRa model of multiple representations to explain how experts use diagrammatic and verbal representations to complement each other. In this model, pictorial information consists of a bitmap and associated node-link structures.…”

Spatial and temporal knowledge representation

“…In time, by contrast, the analogous concept to shape (of an interval or event) is virtually empty. The second reason for the delayed development of spatial KR has a rather specific origin in the 'poverty conjecture' of Forbus et al (1987), that 'there is no problem-independent, purely qualitative representation of space or shape' (Forbus 1995). Forbus adduces this as an explanation for the fact that we humans are so reliant on diagrams and other perceptual representations for our spatial reasoning, since these can capture metric properties absent from a purely qualitative representation, and it is clear that many spatial reasoning tasks cannot be accomplished without access to at least some metric information.…”

Model-Based Reasoning

“…Our model simulates visual operations such as object combination, rotation, and imagined motion, as well as mapping of scenes in dynamic visual analogies. The scene graph representation makes possible a computationally and psychologically richer account of mental imagery than has previously been achieved in cognitive science and artificial intelligence (see Chella, Frixione, and Gaglo, 2000;Davies and Goel, 2000;Forbus, 1995;Funt, 1989;Glasgow, Narayanan, and Chandrasekaran, 1995;Tabachneck-Schuf, Leonardo, and Simon, 1997). …”