Abstract
The theory of mereology and its topological extensions, called mereotopologies, are point-free approaches that allow to model information while avoiding several puzzling assumptions typical of set-theoretical systems. Although points can be introduced in a mereology or mereotopology, the idea is that one does so only when their existence is clearly motivated. The Region Connection Calculus, RCC, is a mereotopological system that assumes upfront the existence of points: points must be accepted for the system to have the desired semantics. This is awkward from the mereological viewpoint and is considered unsatisfactory from the cognitive and the philosophical perspectives on which mereology rests.
We prove that, in dimension two and with the standard semantics, a theory equivalent to RCC can be given without any reference to points at the semantic level also. The theory, based on mereology, uses the topological primitive ‘being a simple region’ (aka ‘being strongly self-connected’).
This is a preview of subscription content, log in via an institution to check access.
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
Bennett, B.: Carving up space: Steps towards construction of an absolutely complete theory of spatial regions. In: Alferes, J.J., Pereira, L.M., Orlowska, E. (eds.) JELIA 1996. LNCS, vol. 1126, pp. 337–353. Springer, Heidelberg (1996)
Borgo, S., Guarino, N., Masolo, C.: A pointless theory of space based on strong connection and congruence. In: Carlucci Aiello, L., Doyle, J., Shapiro, S.C. (eds.) International Conference on Principles of Knowledge Representation and Reasoning (KR 1996), Boston, MA, pp. 220–229. Morgan Kaufmann (1996)
Borgo, S., Guarino, N., Masolo, C.: Qualitative spatial modelling based on parthood, strong connection and congruence. Technical Report Internal Report 03/97, LADSEB-CNR, March 1997 (1997)
Casati, R., Varzi, A.C.: Parts and Places. The Structure of Spatial Representation. MIT Press, Cambridge, MA (1999)
Cohn, A.G., Renz, J.: Qualitative spatial representation and reasoning. In: van Harmelen, F., et al. (eds.) Handbook of Knowledge Representation, pp. 551–596. Elsevier (2007)
Dugat, V., Gambarotto, P., Larvor, Y.: Qualitative theory of shape and structure. Progress in Artificial Intelligence, 850–850 (1999)
Eschenbach, C.: A predication calculus for qualitative spatial representations. In: Freksa, C., Mark, D.M. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 157–172. Springer, Heidelberg (1999)
Galton, A.: Towards a qualitative theory of movement. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 377–396. Springer, Heidelberg (1995)
Galton, A.: Spatial and temporal knowledge representation. Earth Science Informatics 2(3), 169–187 (2009)
Gotts, N.M.: How far can we ‘C’? defining a ‘doughnut’ using connection alone. In: Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning (KR 1994). Morgan Kaufmann (1994)
Gotts, N.M.: Formalizing commonsense topology: The inch calculus. In: Kautz, H., Selman, B. (eds.) International Symposium on Artificial Intelligence and Mathematics (AI/MATH 1996), pp. 72–75 (1996)
Kontchakov, R., Nenov, Y., Pratt-Hartmann, I., Zakharyaschev, M.: On the decidability of connectedness constraints in 2D and 3D euclidean spaces. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI 2011, vol. Two, pp. 957–962. AAAI Press (2011)
Kontchakov, R., Pratt-Hartmann, I., Zakharyaschev, M.: Interpreting Topological Logics over Euclidean Space. In: Twelfth International Conference on Principles of Knowledge Representation and Reasoning, KR 2010 (2010)
Muller, P.: Topological Spatio–Temporal Reasoning and Representation. Computational Intelligence 18(3), 420–450 (2002)
Munkres, J.R.: Topology, 2nd edn. Prentice Hall (2000)
Nenov, Y., Pratt-Hartmann, I.: On the computability of region-based euclidean logics. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 439–453. Springer, Heidelberg (2010)
Pratt-Hartmann, I.: First-order mereotopology. In: Aiello, M., Pratt-Hartmann, I., van Benthem, J. (eds.) Handbook of Spatial Logics, pp. 13–97. Springer (2007)
Pratt-Hartmann, I., Schoop, D.: Elementary polyhedral mereotopology. Journal of Philosophical Logic 31, 469–498 (2002)
Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connections. In: Nebel, B., Rich, C., Swartout, W. (eds.) International Conference on Principles of Knowledge Representation and Reasoning (KR 1992), pp. 165–176. Morgan Kaufmann (1992)
Renz, J., Rauh, R., Knauff, M.: Towards cognitive adequacy of topological spatial relations. In: Habel, C., Brauer, W., Freksa, C., Wender, K.F. (eds.) Spatial Cognition 2000. LNCS (LNAI), vol. 1849, pp. 184–197. Springer, Heidelberg (2000)
Stell, J.G.: Boolean connection algebras: a new approach to the region-connection calculus. Artificial Intelligence 122, 111–136 (2000)
Stell, J.G.: Boolean connection algebras; a new approach to the region-connection calculus. Artificial Intelligence 122, 111–136 (2000)
Stell, J.G., Worboys, M.F.: The algebraic structure of sets of regions. In: Spatial Information Theory A Theoretical Basis for GIS, pp. 163–174. Springer (1997)
Thompson, R.J., Oosterom, P.: Connectivity in the regular polytope representation. GeoInformatica 15(2), 223–246 (2009)
Varzi, A.C.: Spatial reasoning and ontology: Parts, wholes, and locations. In: Aiello, M., Pratt-Hartmann, I., van Benthem, J. (eds.) Handbook of Spatial Logics, pp. 945–1038. Springer (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Borgo, S. (2013). RCC and the Theory of Simple Regions in ℝ2 . In: Tenbrink, T., Stell, J., Galton, A., Wood, Z. (eds) Spatial Information Theory. COSIT 2013. Lecture Notes in Computer Science, vol 8116. Springer, Cham. https://doi.org/10.1007/978-3-319-01790-7_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-01790-7_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01789-1
Online ISBN: 978-3-319-01790-7
eBook Packages: Computer ScienceComputer Science (R0)