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.
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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.
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.
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.
Casati R., Varzi A. C., Holes and Other Superficialities, Cambridge, Mass.: MIT Press/Bradford Books, in press.
Clarke B. L., ‘A Calculus of Individuals Based on “Connection”', Notre Dame Journal of Formal Logic, 22 (1981), 204–218.
Clarke B. L., ‘Individuals and Points', Notre Dame Journal of Formal Logic, 26 (1985), 61–75.
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.
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.
De Laguna T. ‘Point, Line, and Surface, as Sets of Solids', Journal of Philosophy, 19 (1922), 449–61.
Eberle R. A., Nominalistic Systems, Dordrecht: Reidel, 1970.
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.
Herskovits A., Language and Spatial Cognition. An Interdisciplinary Study of the Prepositions in English, Cambridge: Cambridge University Press, 1986.
Hoffman D. D., Richards W. A., ‘Parts of Recognition', Cognition, 18 (1985), 65–96.
Jackson F., Perception. A Representative Theory, Cambridge: Cambridge University Press, 1977.
Leonard H. S., Goodman N., ‘The Calculus of Individuals and Its Uses', Journal of Symbolic Logic, 5 (1940), 45–55.
Leśniewski S., Podstawy ogólnej teoryi mnogości. I, Moskow: Prace Polskiego Kola Naukowego w Moskwie, Sekcya matematyczno-przyrodnicza, 1916.
Lewis D. K., Lewis S. R., ‘Holes', Australasian Journal of Philosophy, 48 (1970), 206–212.
Randell D. A., Analysing the Familiar: Reasoning about Space and Time in the Everyday World, University of Warwick: PhD Thesis, 1991.
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.
Randell D. A., Cohn A. G., ‘Exploiting Lattices in a Theory of Space and Time', Computers and Mathematics with Applications, 23 (1992), 459–476.
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.
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.
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.
Simons P., Parts. A Study in Ontology, Oxford: Clarendon, 1987.
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.
Tiles J. E., Things That Happen, Aberdeen: Aberdeen University Press, 1981.
Tye M., ‘The Adverbial Approach to Visual Experience', Philosophical Review, 93 (1984), 195–225.
Vandeloise C., L'espace en français: sémantique des prépositions spatiales, Paris:Seuil, 1986.
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.
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.
Whitehead A. N., Process and Reality. An Essay in Cosmology, New York: Macmillan, 1929.
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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
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DOI: https://doi.org/10.1007/3-540-57292-9_70
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