Abstract
The Region Connection Calculus (RCC theory) is a well-known spatial representation of topological relations between regions. It claims that the connection relation is primitive in the spatial domain. We argue that the connection relation is indeed primitive to the spatial relations, although in RCC theory there is no room for distance relations. We first analyze some aspects of the RCC theory, e.g. the two axioms in the RCC theory are not strong enough to govern the connection relation, regions in the RCC theory cannot be points, the uniqueness of the \(\iota \) operation in the theory is not guaranteed, etc. To solve some of the problems, we propose an extension to the RCC theory by introducing the notion of region category and adding a new axiom which governs the characteristic property of the connection relation. The extended theory is named as RCC++. We support the claim that the connection relation is primitive to spatial domain by showing how distance relations, size relations are developed in RCC++. At last we revisit a sub-family of un-intended models in RCC theory, argue that RCC++ is more suitable than RCC with regards to its original intended model, and discuss the representation limitation of the RCC, as well as RCC++.
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Bennett, B., Cohn, A. G., Torrini, P., and Hazarika, S. M.: 2000, Region-based Qualitative, Technical Report, School of Computing, University of Leeds.
Bennett, B., Cohn, A. G., Torrini, P., Hazarika, S. M.: 2000, A foundation for region-based qualitative geometry, in W. Horn (ed.), Proceedings of ecai-2000, pp. 204–208.
Clarke, B. L.: 1981, A calculus of individuals based on ‘connection’, Notre Dame Journal of Formal Logic 23(3), 204–218.
Clarke, B. L.: 1985, Individuals and points, Notre Dame Journal of Formal Logic 26(1), 61–75.
Cohn, A. G.: 1993, Modal and non modal qualitative spatial logics, in F. D. Anger, H. W. Guesgen, and J. van Benthem (eds.), Proceedings of the Workshop on Spatial and Temporal Reasoning, Chambéry, IJCAI.
Cohn, A. G.: 1995, A Hierarchical, in A. U. Frank (ed.), Representation of Qualitative Shape based on Connection and Convexity, COSIT’95, LNCS, Springer Verlag, pp. 311–326.
Cohn, A. G., Bennett, B., Gooday, J. M., and Gotts, N.: 1997, RCC: a calculus for region based qualitative spatial reasoning, GeoInformatica 1, 275–316.
Cohn, A. G., and Varzi, A. C.: 2003, Mereotopological connection, Journal of Philosophical Logic 32, 357–390.
de Laguna, T.: 1922, Point, line and surface as sets of solids, The Journal of Philosophy 19:449–461.
Dong, T.: 2005, Recognizing variable spatial environments — the theory of cognitive prism, Ph.D. thesis, Department of Mathematics and Informatics, University of Bremen, Nov. 2005.
Dong, T., and Guesgen, H.: 2007, Is an orientation relation a distance comparison relation?, IJCAI’07 Workshop on Spatial and Temporal Reasoning, Hyderabad, India, pp. 45–51.
Frank, A. U.: 1991, Qualitative spatial reasoning with cardinal directions, Proceedings of the seventh Austrian conference on artificial intelligence, Springer, Berlin, Wien, pp. 157–167.
Frank, A. U.: 1992, Qualitative spatial reasoning about distances and orientations in geographic space, Journal of Visual Langues and Computing 3, 343–371.
Freksa, C.: 1992, Using Orientation Information for Qualitative Spatial Reasoning, Proceedings of the International Conference GIS-From Space to Territory: Theories and Methods of Spatial-Temporal Reasoning, LNCS, Springer, Pisa, September.
Freksa, C.: 1999, Links vor – prototyp oder gebiet?, in G. Hg. Richheit (ed.), Richtungen im raum, Westdeutscher Verlag, Wiesbaden, pp. 231–246.
Gooday, J. M., and Cohn, A. G.: 1994, Conceptual Neighbourhoods in Spatial and Temporal Reasoning, Proceedings ECAI-94 Workshop on Spatial and Temporal Reasoning, Rodríguez, R.
Gotts, N. M.: 1994, How far can we C?, in J. Doyle, E. Sandewall, and P. Torasso (eds.), defining a ‘doughnut’ using connection alone, Principles of knowledge representation and reasoning: Proceedings of the 4th international conference (kr94), San Francisco: Morgan Kaufmann.
Hernández, D.: 1994, Qualitative Representation of Spatial Knowledge. Springer, New York.
Levinson, S.: 1996, Frames of reference and molyneux’s question: Cross-linguistic evidence, in P. Bloom, M. A. Peterson, L. Nadel, and M. F. Garrett (eds.), Space and language, MIT Press, Cambridge, pp. 109–169.
Littré, P. E.: 1874, Dictionnaire de la langue française, Librairie Hachette Et CIE, Paris.
Pfeifer, W., Braum, W., Hagen, G., Huber, A., Müller, K., Petermann, H., Pfeifer, G., Schröter, D., and Schröter, U.: 1989, Etymologisches wörterbuch des deutschen, Akademie-Verlag, Berlin.
Randell, D. A., Cui, Z., and Cohn, A. G.: 1992, A spatial logic based on regions and connection, in B. Nebel, W. Swartout, and C. Rich (eds.), Proceeding 3rd International Conference on Knowledge Representation and Reasoning, Morgan Kaufmann, San Mateo, pp. 165–176.
Renz, J., and Mitra, D.: 2004, Qualitative direction calculi with arbitrary granularity, in C. Zhang, H. Guesgen, and W. Yeap (eds), PRICAI 2004: Trends in Artificial Intelligence: 8th Pacific RIM International Conference on Artificial Intelligence, Springer Berlin, Heidelberg, New Zealand, pp. 65–74.
Russell, B.: 1956, Logic and Knowledge, Routledge, an imprint of Taylor & Francis Books Ltd.
Smith, B.: 1996, Mereotopology: A Theory of Parts and Boundaries, Data and Knowledge Engineering 20, 287–303.
Smith, B.: 2001, Fiat objects, Topoi, 20(2), 131–148.
Woolf, H. B. (ed.): 1980, Webster’s new collegiate dictionary, G. & C. Merriam Company, Springfield, MA, USA.
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Dong, T. A COMMENT ON RCC: FROM RCC TO RCC++ . J Philos Logic 37, 319–352 (2008). https://doi.org/10.1007/s10992-007-9074-y
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DOI: https://doi.org/10.1007/s10992-007-9074-y