1990 年 5 巻 4 号 p. 449-461
One of the fundamental problems in qualitative reasoning is to represent n-dimensional variable spaces. Generally states of a physical system are represented by hypersurfaces in an n-dimensional space, and it is difficult to represent such a situation by using direct product spaces of conventional one-dimensional qualitative values. This paper presents a qualitative representation and reasoning method for three-dimensional variable spaces. The notions of 'multivariant qualitative space' and 'qualitative region,' which are extensions of the quantity space and the qualitative value in one-dimensional space respectively, are used to describe physical situations. Multivariant qualitative spaces consist of qualitative regions and their topological relations, besides 'characteristic vectors' for each qualitative region. We describe a state of a physical system as a 'positional vector' whose value is defined as qualitative regions in a certain multivariant qualitative space, and each qualitative region corresponds to a possible state of the physical system. We can reason about behaviors of the physical system as transitions among qualitative regions, by using characteristic vectors and time derivations of positional vectors, based on the operations of qualitative vectors, i. e., scalar product and vector product. The method is applied to reasoning about the motion of a box sliding and rotating around an edge. The configuration space of possible motions of the box is represented by a multivariant qualitative space, and the reasoner predicts geometric transitions of the box. Since the method is constructed on symbolic inference and requires no numerical information, we can expect that it would be a basic technique for CAD systems of mechanical devices in conceptual design stages.
