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The kinematics of cutting solid objects

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Abstract

This paper studies how the cutting of one solid object by another can be described in a formal theory. We present two alternative first-order representations for this domain. The first views an object as gradually changing its shape until it is split, at which time the original object ceases to exist and two (or more) new objects come into existence. The second focuses instead on chunks of material which are part of the overall object. A chunk persists with constant shape until some pieces of it is cut away, when the chunk ceases to exist. We prove that the two theories are equivalent under ordinary circumstances, and we show that they are sufficient to support some simple commonsense inferences and algorithms.

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References

  1. E. Davis, A logical framework for commonsense predictions of solid object behavior, AI in Eng. 3(1988)125–140.

    Google Scholar 

  2. E. Davis,Representations of Commonsense Knowledge (Kaufmann, San Mateo, CA, 1990).

    Google Scholar 

  3. E. Davis, Infinite loops in finite time: Some observations, in:Proc. 3rd Int. Symp. on Principle of Knowledge Representation and Reasoning, ed. B. Rich, C. Nebel and W. Swartout (Kaufmann, 1992).

  4. B. Faltings, Qualitative kinematics in mechanisms,Proc. 10th IJCAI (1987) pp. 436–442.

  5. C. Hoffmann,Geometric and Solid Modelling (Kaufmann, San Mateo, CA, 1990).

    Google Scholar 

  6. L. Joskowicz, Shape and function in mechanical devices,Proc. 6th AAAI (1987) pp. 611–618.

  7. D. McDermott, A temporal logical for reasoning about processes and plans, Cognitive Sci. 2(1982)277–282.

    Google Scholar 

  8. A.A.G. Requicha, Representations for rigid solids: Theory, methods and systems, ACM Computing Surveys 12(1980)437–464.

    Google Scholar 

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Authors and Affiliations

  1. Courant Institute, 10012, New York, NY, USA

    Ernest Davis

Authors
  1. Ernest Davis
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Additional information

This research has been supported by NSF Grant No. IRI-9001447.

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Davis, E. The kinematics of cutting solid objects. Ann Math Artif Intell 9, 253–305 (1993). https://doi.org/10.1007/BF01530935

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  • DOI: https://doi.org/10.1007/BF01530935

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