Abstract
It has now been clear for some time that for many qualitative spatial or temporal calculi, for instance the well-known RCC8 calculus, the operation of composition of relations which is used is actually only weak composition, which is defined as the strongest relation in the calculus that contains the real composition. An immediate consequence for qualitative calculi where weak composition is not equivalent to composition is that the well-known concept of path-consistency is not applicable anymore. In these cases we can only use algebraic closure which corresponds to applying the path-consistency algorithm with weak composition instead of composition.
In this paper we analyse the effects of having weak compositions. Starting with atomic CSPs, we show under which conditions algebraic closure can be used to decide consistency in a qualitative calculus, how weak consistency affects different important techniques for analysing qualitative calculi and under which conditions these techniques can be applied. For our analysis we introduce a new concept for qualitative relations, the “closure under constraints”. It turns out that the most important property of a qualitative calculus is not whether weak composition is equivalent to composition, but whether the relations are closed under constraints. All our results are general and can be applied to all existing and future qualitative spatial and temporal calculi. We close our paper with a road map of how qualitative calculi should be analysed. As a side effect it turns out that some results in the literature have to be reconsidered.
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References
Allen, J.F.: Maintaining knowledge about temporal intervals. Communications of the ACM 26(11), 832–843 (1983)
Balbiani, P., Osmani, A.: A model for reasoning about topologic relations between cyclic intervals. In: Proceedings of KR 2000, Breckenridge, Colorado (2000)
Balbiani, P., Condotta, J.-F., Farinas del Cerro, L.: A tractable subclass of the block algebra: constraint propagation and preconvex relations. In: Proceedings of the 9th Portuguese Conference on Artificial Intelligence, pp. 75–89 (1999)
Bennett, B.: Some observations and puzzles about composing spatial and temporal relations. In: Proceedings ECAI 1994 Workshop on Spatial and Temporal Reasoning (1994)
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)
Düntsch, I., Wang, H., McCloskey, S.: A relation - algebraic approach to the region connection calculus. Theoretical Computer Science 255(1-2), 63–83 (2001)
Freuder, E.C.: Synthesizing constraint expressions. Communications of the ACM 21(11), 958–965 (1992)
Grigni, M., Papadias, D., Papadimitriou, C.: Topological inference. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montreal, Canada, August 1995, pp. 901–906 (1995)
Guesgen, H.: Spatial reasoning based on Allen’s temporal logic. Technical Report TR-89-049, ICSI, Berkeley, CA (1989)
Ladkin, P.B., Maddux, R.D.: On binary constraint problems. Journal of the ACM 41(3), 435–469 (1993)
Li, S., Ying, M.: Region connection calculus: Its models and composition table. Artificial Intelligence 145(1-2), 121–146 (2003)
Ligozat, G., Renz, J.: What is a qualitative calculus? A general framework. In: Zhang, C., Guesgen, H.W., Yeap, W.-K. (eds.) PRICAI 2004. LNCS (LNAI), vol. 3157, pp. 53–64. Springer, Heidelberg (2004)
Ligozat, G.: When tables tell it all: Qualitative spatial and temporal reasoning based on linear orderings. In: Montello, D.R. (ed.) COSIT 2001. LNCS, vol. 2205, pp. 60–75. Springer, Heidelberg (2001)
Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8, 99–118 (1977)
Montanari, U.: Networks of constraints: Fundamental properties and applications to picture processing. Information Sciences 7, 95–132 (1974)
Navarrete, I., Sattar, A., Wetprasit, R., Marin, R.: On point-duration networks for temporal reasoning. Artificial Intelligence 140(1-2), 39–70 (2002)
Pujari, A.K., Vijaya Kumari, G., Sattar, A.: INDU: An Interval and Duration Network. In: Australian Joint Conference on Artificial Intelligence, pp. 291–303 (1999)
Pujari, A.K., Sattar, A.: A new framework for reasoning about points, intervals and durations. In: Thomas, D. (ed.) Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 1259–1267. Morgan Kaufmann Publishers, San Francisco (1999)
Randell, D., Cui, Z., Cohn, T.: A spatial logic based on regions and connection. In: Proceedings of KR 1992, San Mateo, CA, pp. 165–176. Morgan Kaufmann, San Francisco (1992)
Renz, J.: Maximal tractable fragments of the region connection calculus: A complete analysis. In: Proceedings of IJCAI 1999, pp. 448–455 (1999)
Renz, J., Mitra, D.: Qualitative direction calculi with arbitrary granularity. In: Zhang, C., Guesgen, H.W., Yeap, W.-K. (eds.) PRICAI 2004. LNCS (LNAI), vol. 3157, pp. 65–74. Springer, Heidelberg (2004)
Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: A maximal tractable fragment of the Region Connection Calculus. Artificial Intelligence 108(1-2), 69–123 (1999)
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Renz, J., Ligozat, G. (2005). Weak Composition for Qualitative Spatial and Temporal Reasoning. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_40
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DOI: https://doi.org/10.1007/11564751_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29238-8
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