Abstract
The way we use spatial descriptions in many everyday situations is of a qualitative nature. This is often achieved by specifying spatial relations between objects or regions. The advantage of using qualitative descriptions is that we can be less precise and thereby less prone to making an error. For example, it is often easier to decide whether an object is inside another object than to specify exactly where the first object is with respect to the second one. In artificial intelligence, a variety of formalisms have been developed that deal with space on the basis of relations between objects or regions that objects might occupy. One of these formalisms is the RCC theory, which is based on a primitive relation, called connectedness, and uses a set of topological relations, defined on the basis of connectedness, to provide a framework for reasoning about regions. This paper discusses an extension of the RCC theory based on fuzzy logic, which enables us to express preferences among spatial descriptions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allen, J.: Maintaining knowledge about temporal intervals. Commun. ACM 26, 832–843 (1983)
Bloch, I.: Spatial representation of spatial relationship knowledge. In: Proc. KR 2000, pp. 247–258. Breckenridge, Colorado (2000)
Bloch, I.: Fuzzy spatial relationships for image processing and interpretation: A review. Image and Vision Computing 23, 89–110 (2005)
Brewka, G.: Preferred subtheories: An extended logical framework for default reasoning. In: Proc. IJCAI 1989, pp. 1043–1048 (1989)
Cohn, A., Bennett, B., Gooday, J., Gotts, N.: Representing and reasoning with qualitative spatial relations about regions. In: Stock, O. (ed.) Spatial and Temporal Reasoning, pp. 97–134. Kluwer, Dordrecht (1997)
Cohn, A., Gotts, N.: The ‘Egg-Yolk’ representation of regions with indeterminate boundaries. In: Burrough, P., Frank, A. (eds.) Geographical Objects with Undetermined Boundaries. GISDATA Series, vol. 2, pp. 171–187. Taylor and Francis, London (1996)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, London (1980)
Egenhofer, M., Al-Taha, K.: Reasoning about gradual changes of topological relationships. In: Frank, A.U., Campari, I., Formentini, U. (eds.) GIS 1992. LNCS, vol. 639, pp. 196–219. Springer, Heidelberg (1992)
Freksa, C.: Temporal reasoning based on semi-intervals. Artificial Intelligence 54, 199–227 (1992)
Freuder, E., Wallace, R.: Partial constraint satisfaction. Artificial Intelligence 58, 21–70 (1992)
Guesgen, H.: Spatial reasoning based on Allen’s temporal logic. Technical Report TR-89-049, ICSI, Berkeley, California (1989)
Guesgen, H., Hertzberg, J.: Spatial persistence. Applied Intelligence (Special Issue on Spatial and Temporal Reasoning) 6, 11–28 (1996)
Guesgen, H., Hertzberg, J., Philpott, A.: Towards implementing fuzzy Allen relations. In: Proc. ECAI-94 Workshop on Spatial and Temporal Reasoning, Amsterdam, The Netherlands, pp. 49–55 (1994)
Klir, G., Folger, T.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs (1988)
Lehmann, F., Cohn, A.: The EGG/YOLK reliability hierarchy: Semantic data integration using sorts with prototypes. In: Proc. 3rd International Conference on Information and Knowledge Management (CIKM 1994), pp. 272–279. Gaithersburg, Maryland (1994)
Ligozat, G. (ed.): Qualitative Spatial and Temporal Reasoning. Wiley-ISTE, Hoboken (2011)
Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Proc. KR 1992, pp. 165–176. Cambridge, Massachusetts (1992)
Renz, J.: A spatial odyssey of the interval algebra: 1. directed intervals. In: Proc. IJCAI 2001, pp. 51–56. Seattle, Washington (2001)
Schockaert, S., De Cock, M., Cornelis, C., Kerre, E.: Fuzzy region connection calculus: Representing vague topological information. Journal of Approximate Reasoning 48, 314–331 (2008)
Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Guesgen, H.W. (2015). A Fuzzy Set Approach to Expressing Preferences in Spatial Reasoning. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. Lecture Notes in Computer Science(), vol 9060. Springer, Cham. https://doi.org/10.1007/978-3-319-14726-0_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-14726-0_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-14725-3
Online ISBN: 978-3-319-14726-0
eBook Packages: Computer ScienceComputer Science (R0)