Abstract
The distinction between object-based and field-based conceptions of geographical reality has become well-known in recent years. It replicates at a conceptual level the distinction between vector-based and raster-based implementation methods for GIS. In this paper I endeavour to lay the groundwork for a careful, mathematically rigorous development of the relevant ideas at the conceptual level. The notions of object and field are given precise mathematical definitions, and an appropriate formal apparatus is constructed by which to address such issues as the interconvertibility of the object-based and field-based paradigms, and their relative adequacy for different representational problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Asher, N. & Vieu, L. (1995), Toward a geometry of common sense: A semantics and a complete axiomatisation of mereotopology, in C. S. Mellish, ed., ‘Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI’95)’, Morgan Kaufmann, San Mateo, Calif., pp. 846–52.
Borgo, S., Guarino, N. & Masolo, C. (1996), A pointless theory of space based on strong connection and congruence, in L. C. Aiello, J. Doyle & S. Shapiro, eds, ‘Principles of Knowledge Representation and Reasoning: Proceedings of the Fifth International Conference (KR’96)’, Morgan Kaufmann, San Francisco, CA, pp. 220–29.
Casati, R. & Varzi, A. (1999), Parts and Places: The Structures of Spatial Representation, MIT Press, Cambridge, Mass. and London.
Couclelis, H. (1992), People manipulate objects (but cultivate fields): Beyond the raster-vector debate in GIS, in A. U. Frank, I. Campari & U. Formentini, eds, ‘Theories and Methods of Spatio-Temporal Reasoning in Geographic Space’, Vol. 639 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, pp. 65–77.
Davis, E. (1990), Representations of Commonsense Knowledge, Morgan Kaufmann, San Mateo, Calif.
Galton, A. (2001), ‘Space, time, and the representation of geographical reality’, Topoi.
Kovalevsky, V. A. (1989), ‘Finite topology as applied to image analysis’, Computer Vision, Graphics, and Image Processing 46, 141–61.
Perring, F. H. & Walters, S. M., eds (1962), Atlas of the British Flora, Thomas Nelson & Sons, London.
Peuquet, D. J. (1984), ‘A conceptual framework and comparison of spatial data models’, Cartographica 21(4), 66–113.
Pratt, I. & Lemon, O. (1997), ‘Ontologies for plane, polygonal mereotopology’, Notre Dame Journal of Formal Logic 38(2), 225–45.
Randell, D. A., Cui, Z. & Cohn, A. G. (1992), 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 (KR’92)’, Morgan Kaufmann, San Mateo, Calif., pp. 165–76.
Smith, B. (1993), Ontology and the logistic analysis of reality, in N. Guarino & R. Poli, eds, ‘Proceedings of the International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation’, Institute for Systems Theory and Biomedical Engineering of the Italian National Research Council, Padova, Italy, pp. 51–68.
Worboys, M. F. (1995), GIS: A Computing Perspective, Taylor & Francis, London.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Galton, A. (2001). A Formal Theory of Objects and Fields. In: Montello, D.R. (eds) Spatial Information Theory. COSIT 2001. Lecture Notes in Computer Science, vol 2205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45424-1_31
Download citation
DOI: https://doi.org/10.1007/3-540-45424-1_31
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42613-4
Online ISBN: 978-3-540-45424-3
eBook Packages: Springer Book Archive