Layers: A New Approach to Locating Objects in Space

  • Maureen Donnelly
  • Barry Smith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2825)


Standard theories in mereotopology focus on relations of parthood and connection among spatial or spatio-temporal regions. Objects or processes which might be located in such regions are not normally directly treated in such theories. At best, they are simulated via appeal to distributions of attributes across the regions occupied or by functions from times to regions. The present paper offers a richer framework, in which it is possible to represent directly the relations between entities of various types at different levels, including both objects and the regions they occupy. What results is a layered mereotopology, a theory which can handle multiple layers (analogous to the layers of a lasagna) of spatially or spatiotemporally coincident but mereologically non-overlapping entities.


Ontology mereology mereotopology qualitative spatial reasoning map layers dynamic GIS 


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  1. (Asher and Vieu, 1995).
    Asher, N., Vieu, L.: Towards a Geometry of Commonsense: A Semantics and a Complete Axiomatization of Mereotopology. In: Proceedings of IJCAI 1995, pp. 846–852. Morgan Kaufmann, San Mateo (1995)Google Scholar
  2. (Bennett, 2001).
    Bennett, B.: Space, Time, Matter, and Things. In: (Welty and Smith), pp. 105–116Google Scholar
  3. (Bennett, 2001a).
    Bennett, B.: A Categorical Axiomatization of Region-Based Geometry. Fundamenta Informaticae 46(1-2), 145–158 (2001a)zbMATHMathSciNetGoogle Scholar
  4. (Bittner 2001).
    Bittner, T.: The Qualitative Structure of Built Environments. Fundamenta Informaticae 46, 97–128 (2001)zbMATHMathSciNetGoogle Scholar
  5. (Bittner and Smith, 2002).
    Bittner, T., Smith, B.: A Theory of Granular Partitions. In: Duckham, M., Goodchild, M.F., Worboys, M.F. (eds.) Foundations of Geographic Information Science, pp. 117–151. Taylor & Francis, London (2002)Google Scholar
  6. (Casati and Varzi, 1994).
    Casati, R., Varzi, A.C.: Holes and Other Superficialities. MIT Press, Cambridge (1994)Google Scholar
  7. (Casati and Varzi, 1999).
    Casati, R., Varzi, A.C.: Parts and Places. The Structures of Spatial Representation. MIT Press, Cambridge (1999)Google Scholar
  8. (Casati, Smith and Varzi 1998).
    Asher, N., Vieu, L.: Towards a Geometry of Commonsense: A Semantics and a Complete Axiomatization of Mereotopology. In: Proceedings of IJCAI 1995, pp. 846–852. Morgan Kaufmann, San Mateo (1995)Google Scholar
  9. (Cohn, 2001).
    Cohn, A.G.: Formalizing Bio-Spatial Knowledge. In: (Welty and Smith), pp. 198–209 (2001)Google Scholar
  10. (Cohn and Hazarika 2001).
    Cohn, A.G., Hazarika, S.M.: Continuous Transitions in Mereotopology. In: Commonsense 2001: 5th Symposium on Logical Formalizations of Commonsense Reasoning (2001)(to appear)Google Scholar
  11. (Cohn and Varzi, 1998).
    Cohn, A.G., Varzi, A.C.: Connection Relations in Mereotopology. In: Prade, H. (ed.) Proceedings of the 13th European Conference on Artificial Intelligence (ECAI 1998), pp. 150–154. Wiley, New York (1998)Google Scholar
  12. (Cui et al., 1992)
    Cui, Z., Cohn, A.G., Randell, D.A.: Qualitative Simulation Based on a Logical Formalism of Space and Time. In: Proceedings of AAAI 1992 (1992)Google Scholar
  13. (Donnelly, 2003).
    Donnelly, M.: Layered Mereotopology. In: IJCAI 2003 (2003)ForthcomingGoogle Scholar
  14. (Gotts et al., 1996)
    Gotts, N.M., Gooday, J.M., Cohn, A.G.: A Connection Based Approach to Commonsense Topological Description and Reasoning. The Monist 79, 51–75 (1996)Google Scholar
  15. (Grenon and Smith, 2003).
    Grenon, P., Smith, B.: SNAP and SPAN. A Prolegomena to Geodynamic Ontology. IFOMIS Technical Report, University of Leipzig (2003)Google Scholar
  16. (Mark and Turk, 2003).
    Mark, D.M., Turk, A.: Landscape Categories in Yindjibarndi: Ontology, Environment, and Language. In: Kuhn, W., Worboys, M.F., Timpf, S. (eds.) COSIT 2003. LNCS, vol. 2825, pp. 28–45. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. (Schulz and Hahn, 2001).
    Schulz, S., Hahn, U.: Mereotopological Reasoning about Parts and (W)Holes in Bio-Ontologies. In: (Welty and Smith), pp. 210–221 (2001)Google Scholar
  18. (Simons, 1987).
    Simons, P.M.: Parts: A Study in Ontology. Oxford University Press, Oxford (1987)Google Scholar
  19. (Smith, 1995).
    Smith, B.: On Drawing Lines on a Map. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 475–484. Springer, Heidelberg (1995)Google Scholar
  20. (Smith, 1996).
    Smith, B.: Mereotopology: A Theory of Parts and Boundaries. Data & Knowledge Engineering 20, 287–303 (1996)zbMATHCrossRefGoogle Scholar
  21. (Smith and Grenon, 2003).
    Smith, B., Grenon, P.: The Cornucopia of Formal-Ontological Relations. Dialectica (2003) ForthcomingGoogle Scholar
  22. (Smith and Varzi, 2000).
    Smith, B., Varzi, A.C.: Fiat and Bona Fide Boundaries. Philosophy and Phenomenological Research 60(2), 401–420 (2000)CrossRefGoogle Scholar
  23. (Smith, 2001).
    Smith, B.: Fiat Objects. Topoi 20 (2), 131–148 (2001)CrossRefGoogle Scholar
  24. (Welty and Smith, 2001).
    Proceedings of the 2nd International Conference on Formal Ontology in Information Systems (FOIS 2001). ACM Press, New York (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Maureen Donnelly
    • 1
  • Barry Smith
    • 1
    • 2
  1. 1.Institute for Formal Ontology and Medical Information ScienceUniversity of Leipzig 
  2. 2.Department of PhilosophyUniversity at Buffalo

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