Abstract
To reason about geographical objects, it is not only necessary to have more or less complete information about where these objects are located in space, but also how they can change their position, shape, and size over time. In this paper we investigate how calculi discussed in the field of qualitative spatial reasoning (QSR) can be temporalized in order to gain reasoning formalisms that can be used to express spatial configurations and their dynamics. In a first step, we briefly discuss temporalized spatial constraint languages. In particular, we investigate how the notion of continuous change can be expressed in such languages and how continuous change is represented in the so-called conceptual neighborhood graph of the spatial calculus at hand. In a second step, we focus on a special reasoning problem, which occurs quite naturally in the context of temporalized spatial calculi: Given an initial spatial scenario of some physical objects, which scenarios are accessible if the set of all possible paths of these objects is constrained by some further conditions? We show that for many spatial calculi this general problem cannot be dealt with by using the information encoded in the classical neighborhood graphs, as usually discussed in the literature. Rather, we introduce a generalized concept of neighborhood graph, which allows for reasoning about objects in such dynamic settings.
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References
Allen, J.F.: Maintaining knowledge about temporal intervals. Communications of the ACM 26(11), 832–843 (1983)
Bennett, B.: Space, time, matter and things. In: FOIS, pp. 105–116 (2001)
Bennett, B., Cohn, A.G., Wolter, F., Zakharyaschev, M.: Multi-dimensional modal logic as a framework for spatio-temporal reasoning. Applied Intelligence 17(3), 239–251 (2002)
Bennett, B., Isli, A., Cohn, A.G.: When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In: Proceedings of the IJCAI 1997 Workshop on Spatial and Temporal Reasoning, Nagoya, Japan (1997)
Cohn, A.G.: Qualitative spatial representation and reasoning techniques. In: Brewka, G., Habel, C., Nebel, B. (eds.) KI 1997. LNCS, vol. 1303. Springer, Heidelberg (1997)
Davis, E.: Continuous shape transformation and metrics on regions. Fundamenta Informaticae 46(1-2), 31–54 (2001)
Egenhofer, M.J., Al-Taha, K.K.: Reasoning about gradual changes of topological relationships. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639, pp. 196–219. Springer, Heidelberg (1992)
Erwig, M., Schneider, M.: Spatio-temporal predicates. IEEE Transactions on Knowledge and Data Engineering 14(4), 881–901 (2002)
Freksa, C.: Conceptual neighborhood and its role in temporal and spatial reasoning. In: Decision Support Systems and Qualitative Reasoning, pp. 181–187. North-Holland, Amsterdam (1991)
Gabelaia, D., Kontchakov, R., Kurucz, A., Wolter, F., Zakharyaschev, M.: Combining spatial and temporal logics: Expressiveness vs. complexity. To appear in Journal of Artificial Intelligence Research (2005)
Galton, A.: Qualitative Spatial Change. Oxford University Press, Oxford (2000)
Galton, A.: A generalized topological view of motion in discrete space. Theoretical Compututer Science 305(1-3), 111–134 (2003)
Gerevini, A., Nebel, B.: Qualitative spatio-temporal reasoning with RCC-8 and Allen’s interval calculus: Computational complexity. In: Proceedings of the 15th European Conference on Artificial Intelligence (ECAI-2002), pp. 312–316. IOS Press, Amsterdam (2002)
Knauff, M.: The cognitive adequacy of allen’s interval calculus for qualitative spatial representation and reasoning. Spatial Cognition and Computation 1, 261–290 (1999)
Muller, P.: A qualitative theory of motion based on spatio-temporal primitives. In: Cohn, A.G., Schubert, L.K., Shapiro, S.C. (eds.) Proceedings of the Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR 1998), Trento, Italy, June 2-5, pp. 131–143. Morgan Kaufmann, San Francisco (1998)
Muller, P.: Topological spatio-temporal reasoning and representation. Computational Intelligence 18(3), 420–450 (2002)
Nebel, B., Bürckert, H.-J.: Reasoning about temporal relations: A maximal tractable subclass of Allen’s interval algebra. Technical Report RR-93-11, Deutsches Forschungszentrum für Künstliche Intelligenz GmbH, Kaiserslautern, Germany (1993)
Ragni, M., Wölfl, S.: Branching Allen: Reasoning with intervals in branching time. In: Freksa, C., Knauff, M., Krieg-Brückner, B., Nebel, B., Barkowsky, T. (eds.) Spatial Cognition IV. LNCS (LNAI), vol. 3343, pp. 323–343. Springer, Heidelberg (2005)
Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Nebel, B., Swartout, W., Rich, C. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the 3rd International Conference (KR 1992), pp. 165–176. Morgan Kaufmann, San Francisco (1992)
Vilain, M.B., Kautz, H.A., van Beek, P.G.: Contraint propagation algorithms for temporal reasoning: A revised report. In: Weld, D.S., de Kleer, J. (eds.) Readings in Qualitative Reasoning about Physical Systems, pp. 373–381. Morgan Kaufmann, San Francisco (1989)
Wolter, F., Zakharyaschev, M.: Spatio-temporal representation and reasoning based on RCC-8. In: Cohn, A., Giunchiglia, F., Selman, B. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the 7th International Conference (KR 2000). Morgan Kaufmann, San Francisco (2000)
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Ragni, M., Wölfl, S. (2005). Temporalizing Spatial Calculi: On Generalized Neighborhood Graphs. In: Furbach, U. (eds) KI 2005: Advances in Artificial Intelligence. KI 2005. Lecture Notes in Computer Science(), vol 3698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11551263_7
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DOI: https://doi.org/10.1007/11551263_7
Publisher Name: Springer, Berlin, Heidelberg
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