Skip to main content

Spatial reasoning in a holey world

  • Conference paper
  • First Online:
Advances in Artificial Intelligence (AI*IA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 728))

Included in the following conference series:

Abstract

This paper outlines a basic formalism for reasoning about holes and holed things. Several domains come to interact: ontology (holes are parasitic entities), mereology (holes may bear part-whole relations to one another); topology (holes are one piece things located at the surfaces of their hosts); morphology (holes are fillable). The descriptive power of the resulting framework is illustrated with reference to some issues in the modelling, the representation, and the taxonomy of spatial inclusion.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aurnague M., Vieu L., ‘A Three-Level Approach to the Semantics of Space', in C. Z. Wibbelt (ed.), The Semantics of Preposition: From Mental Processing to Natural Language Processing, Berlin: Mouton de Gruyter, in press.

    Google Scholar 

  2. Bäckström C., ‘Logical Modelling of Simplified Geometrical Objects and Mechanical Assembly Processes', in Su-shing Chen (ed.), Advances in Spatial Reasoning, Volume 1, Norwood: Ablex, 1990, pp. 35–61.

    Google Scholar 

  3. Casati R., Varzi A. C., ‘An Ontology for Superficial Entities, I: Holes', in N. Guarino, R. Poli (eds.), International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation, Padova: Ladseb-CNR, 1993, pp. 127–148.

    Google Scholar 

  4. Casati R., Varzi A. C., Holes and Other Superficialities, Cambridge, Mass.: MIT Press/Bradford Books, in press.

    Google Scholar 

  5. Clarke B. L., ‘A Calculus of Individuals Based on “Connection”', Notre Dame Journal of Formal Logic, 22 (1981), 204–218.

    Google Scholar 

  6. Clarke B. L., ‘Individuals and Points', Notre Dame Journal of Formal Logic, 26 (1985), 61–75.

    Google Scholar 

  7. Cohn A. G., Randell D. A., Cui Z., ‘A Taxonomy of Logically Defined Qualitative Spatial Regions', in N. Guarino, R. Poli (eds.), International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation, Padova: Ladseb-CNR, 1993, pp. 149–158.

    Google Scholar 

  8. Davis E., ‘A Framework for Qualitative Reasoning About Solid Objects', in G. Rodriguez (ed.), Proceedings of the Workshop on Space Telerobotics, Pasadena, Ca.: NASA and JPL, 1987, pp. 369–375.

    Google Scholar 

  9. De Laguna T. ‘Point, Line, and Surface, as Sets of Solids', Journal of Philosophy, 19 (1922), 449–61.

    Google Scholar 

  10. Eberle R. A., Nominalistic Systems, Dordrecht: Reidel, 1970.

    Google Scholar 

  11. Hayes P. J., ‘Naive Physics I: Ontology for Liquids', in J. R. Hobbs, R. C. Moore (eds.), Formal Theories of the Commonsense World, Norwood: Ablex, 1985, pp. 71–107.

    Google Scholar 

  12. Herskovits A., Language and Spatial Cognition. An Interdisciplinary Study of the Prepositions in English, Cambridge: Cambridge University Press, 1986.

    Google Scholar 

  13. Hoffman D. D., Richards W. A., ‘Parts of Recognition', Cognition, 18 (1985), 65–96.

    Google Scholar 

  14. Jackson F., Perception. A Representative Theory, Cambridge: Cambridge University Press, 1977.

    Google Scholar 

  15. Leonard H. S., Goodman N., ‘The Calculus of Individuals and Its Uses', Journal of Symbolic Logic, 5 (1940), 45–55.

    Google Scholar 

  16. Leśniewski S., Podstawy ogólnej teoryi mnogości. I, Moskow: Prace Polskiego Kola Naukowego w Moskwie, Sekcya matematyczno-przyrodnicza, 1916.

    Google Scholar 

  17. Lewis D. K., Lewis S. R., ‘Holes', Australasian Journal of Philosophy, 48 (1970), 206–212.

    Google Scholar 

  18. Randell D. A., Analysing the Familiar: Reasoning about Space and Time in the Everyday World, University of Warwick: PhD Thesis, 1991.

    Google Scholar 

  19. Randell D. A., Cohn A. G., ‘Modelling Topological and Metrical Properties in Physical Processes', in R. J. Brachman, H. J. Levesque, R. Reiter (eds.), Principles of Knowledge Representation and Reasoning. Proceedings of the First International Conference, Los Altos: Morgan Kaufmann, 1989, pp. 357–368.

    Google Scholar 

  20. Randell D. A., Cohn A. G., ‘Exploiting Lattices in a Theory of Space and Time', Computers and Mathematics with Applications, 23 (1992), 459–476.

    Google Scholar 

  21. Randell D. A., Cui Z., Cohn A. G., ‘An Interval Logic of Space Based on “Connection”', in B. Neumann (ed.), Proceedings of the 10th European Conference on Artificial Intelligence, Chichester: John Wiley & Sons, 1992, pp. 394–398.

    Google Scholar 

  22. Randell D. A., Cui Z., Cohn A. G., ‘A Spatial Logic Based on Regions and Connection', in B. Nebel, C. Rich, W. Swartout (eds.), Principles of Knowledge Representation and Reasoning. Proceedings of the Third International Conference, Los Altos: Morgan Kaufmann, 1992, pp. 165–176.

    Google Scholar 

  23. Shoham Y., ‘Naive Kinematics: Two Aspects of Shape', in J. R. Hobbs (ed.), Commonsense Summer: Final Report, Technical Report # CSLI-85-35, Stanford: SRI International, AI Center, 1985, pp. 4:1–25.

    Google Scholar 

  24. Simons P., Parts. A Study in Ontology, Oxford: Clarendon, 1987.

    Google Scholar 

  25. Smith B., ‘Ontology and the Logistic Analysis of Reality', in N. Guarino, R. Poli (eds.), International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation, Padova: Ladseb-CNR, 1993, pp. 51–68.

    Google Scholar 

  26. Tiles J. E., Things That Happen, Aberdeen: Aberdeen University Press, 1981.

    Google Scholar 

  27. Tye M., ‘The Adverbial Approach to Visual Experience', Philosophical Review, 93 (1984), 195–225.

    Google Scholar 

  28. Vandeloise C., L'espace en français: sémantique des prépositions spatiales, Paris:Seuil, 1986.

    Google Scholar 

  29. Varzi A., ‘On the Boundary Between Mereology and Topology', in B. Smith, R. Casati (eds.), Philosophy and the Cognitive Sciences. Proceedings of the 16th International Wittgenstein Symposium, Vienna: Hölder-Pichler-Tempsky, to appear.

    Google Scholar 

  30. Vieu L., Sémantique des relations spatiales et inférences spatio-temporelles: Une contribution á l'étude des structures formelles de l'espace en Langage Naturel, Université Paul Sabatier de Toulouse: PhD Thesis, 1991.

    Google Scholar 

  31. Whitehead A. N., Process and Reality. An Essay in Cosmology, New York: Macmillan, 1929.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Pietro Torasso

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Varzi, A.C. (1993). Spatial reasoning in a holey world. In: Torasso, P. (eds) Advances in Artificial Intelligence. AI*IA 1993. Lecture Notes in Computer Science, vol 728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57292-9_70

Download citation

  • DOI: https://doi.org/10.1007/3-540-57292-9_70

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57292-3

  • Online ISBN: 978-3-540-48038-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics