Bäckström, C. (1987). Logical Modelling of Simplified Geometrical Objects and Mechanical Assembly Processes. Technical Report LiTH-IDA-R-87-05, Department of Computer and Information Science, Linköping University, Sweden. Also published in Spatial Reasoning, vol. 1" ed. Su-shing Chen, Ablex. (bibtex),
Abstract: This paper describes a logical model for geometric reasoning about assembly processes in a simplified world called the 2D+ world. The 2D+ world is a restricted 2+-dimensional world, which is powerful enough to express most of the interesting assembly problems. A static description of this world in first order predicate calculus, and a dynamic description of assembly operations is provided. Assembly operations are expressed in a dynamic logic, extended with two new very restrictedly used operators to attack the frame problem. An algorithm for verifying sequences of assembly operations is also provided.The reason for using a logical geometry model instead of the usual procedural models, is that logical descriptions are better suited to symbolic reasoning than procedural ones. This is especially important since the combination of geometric and symbolic reasoning (geombolic reasoning) is known to be a very hard problem.
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