Abstract
Ordering information is a special type of spatial information that derives from the linear, planar or spatial ordering of points. A definition of ordering information in terms of the orientation of simplexes is used in this paper to introduce a system of line segment relations which generalizes Allen's system of interval relations to two dimensions. It shows that this generalization differs in interesting properties from the generalizations based on topological relations which have been proposed so far. The conceptual neighborhood structure of the line segment relations provides the foundation of ordering information reasoning. This is illustrated with an example from motion planning. Finally, the problem of representing ordering information is addressed. In that context the cell complex representation of Frank and Kuhn is compared with the approach presented here.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Allen, J. (1983). Maintaining knowledge about temporal intervals. Comm. of the ACM, 26, 832–843.
Egenhofer, M. & Franzosa, R. (1991). Point-set topological spatial relations, International Journal of Geographical Information Systems, 5, 161–174.
Frank, A. & Kuhn, W. (1986). Cell graphs: A provable correct method for the storage of geometry. In Proc. 2nd International Symposium on Spatial Data Handling, Seattle, WA, 411–436
Freksa, C. (1992). Temporal reasoning based on semi-intervals. Artificial Intelligence, 54, 199–227.
Freksa, C., & Röhrig, R. (1993). Dimensions of qualitative spatial reasoning. In N. Piera Carreté & M. Singh (Eds.), Qualitative reasoning and decision technologies (pp. 483–492). Barcelona: CIMNE.
Güsgen, H. (1989). Spatial reasoning based on Allen's temporal logic. TR-89-049, ISCI, Berkeley, CA
Hernandez, D. (1992). Qualitative representation of spatial knowledge, Ph.D. thesis, TU München.
Goodman, J., & Pollack, R. (1993). Allowable sequences and order types in discrete and computational geometry. In J. Pach (Ed.), New trends in discrete and computational geometry (pp. 103–134)
Randell, D. & Conn, T. (1989). Modelling topological and metrical properties in physical processes. In R. Brachman et al. (eds.) Principles of Knowledge Representation and Reasoning
Randell, D., Cui, Z. and Cohn, A. (1992). A Spatial Logic based on Regions and Connection, In Proc 3rd Int. Conf on Knowledge Representation and Reasoning, Boston
Schlieder, C. (1993). Representing visible locations for qualitative navigation. In N. Piera Carrete & M. Singh (Eds.), Qualitative Reasoning and Decision Technologies (pp. 523–532). Barcelona: CIMNE.
Schlieder, C. (1995). Qualitative shape representation In A. Frank (ed.) Spatial conceptual models for geographic objects with undetermined boundaries, London: Taylor & Francis.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schlieder, C. (1995). Reasoning about ordering. In: Frank, A.U., Kuhn, W. (eds) Spatial Information Theory A Theoretical Basis for GIS. COSIT 1995. Lecture Notes in Computer Science, vol 988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60392-1_22
Download citation
DOI: https://doi.org/10.1007/3-540-60392-1_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60392-4
Online ISBN: 978-3-540-45519-6
eBook Packages: Springer Book Archive