Abstract
In qualitative spatial reasoning, the last ten years have brought a lot of results on theories of spatial properties and relations taking regions of space as primitive entities. In particular, the axiomatization of mereotopologies has been extensively studied. However, properties of space such as divisibility, density and atomicity haven’t attracted much attention in this context. Nevertheless, atomicity is especially important if one seeks to build a bridge between spatial reasoning and spatial databases approaches in areas like vision or GIS. In this paper we will investigate the possibility of characterizing such properties in spaces modeled by mereologies and mereotopologies. In addition, properties of atoms like extension and self-connectedness will be considered.
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
Asher, N., Vieu, L.: Toward a Geometry of Common Sense: A Semantics and a Complete Axiomatization of Mereotopology. In: Proceedings of IJCAI’95. Morgan Kaufmann, San Mateo (CA) (1995) 846–852
Beltmandt, Z.: Manuel de prètopologie. Hermés, Paris (1993)
Borgo, S., Guarino, N., Masolo, C.: A Pointless Theory of Space Based on Strong Connection and Congruence. In: L. Carlucci Aiello & S. Shapiro (eds.), Principles of Knowledge Representation and Reasoning. Proceedings of KR’96, Morgan Kauffmann, San Mateo (CA) (1996) 220–229
Casati, R., Varzi, A.C.: Holes and Other Superficialities. The MIT Press, Cambridge (MA) (1994)
Clarke, B.L.: A calculus of individuals based on ”connection“. Notre Dame Journal of Formal Logic 22(3) (1981) 204–218
Clarke, B.L.: Individuals and points. Notre Dame Journal of Formal Logic 26(1) (1985) 61–75
Cohn, A., Varzi,: A. Connection Relations in Mereotopology. In: H. Prade (ed.) Proceedings of ECAI’98. Wiley, (1998) 150–154
Gotts, N.: How far can we “C”? Defining a “doughnut” using connection alone. In: J. Doyle, E. Sandewall & P. Torasso (eds.), Principles of Knowledge Representation and Reasoning. Proceedings of KR’94. Morgan Kaufmann, San Mateo (CA) (1994) 246–257
Grünbaum, B., Shephard, G.C.: Tilings and patterns. Freeman, New York (1987)
Lesniewski, S.: O podstawach matematyki [On the Foundations of Mathematics]. Przeglad Filosoficzny [Philosophical Review] (1927-193) 30–34
Pratt, I., Lemon, O.: Ontologies for Plane, Polygonal Mereotopology. Notre Dame Journal of Formal Logic 38(2) (1997) 225–245
Pyle, A.: Atomism and its critics. Thoemmes Press, Bristol (1995)
Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: B. Nebel, C. Rich & W. Swartout (eds.), Principles of Knowledge Representation and Reasoning, Proceedings of KR’92. Morgan Kaufmann, San Mateo (CA) (1992) 165–176
Simons, P.: Parts-A study in ontology. Clarendon Press Oxford (1987)
Smith, B.: Basic concepts of formal ontology. In: N. Guarino (ed.) Formal Ontology in Information Systems (FOIS’98). IOS Press, Amsterdam (1998) 19–28
Sorabji, R.: Time, creation and the continuum; theories in antiquity and the early middle ages. Duckworth, London (1983)
Stell, J.G.: A Lattice Theoretic Account of Spatial Regions. Technical Report, Departement of Computer Science, Keele University (1997)
Tarski, A.: Logic, semantics, metamathematics. Papers from 1923 to 1938. Clarendon Press, Oxford (1956)
Tiles, G.E.: Things that happen. Aberdeen University Press, Aberdeen (1981)
Varzi, A.: Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology. Data and Knowledge Engineering 20(3) (1996) 259–286
Whitehead, A.: An enquiry concerning the principles of natural knowledge. Cambridge University Press, Cambridge (dy1919).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Masolo, C., Vieu, L. (1999). Atomicity vs. Infinite Divisibility of Space. In: Freksa, C., Mark, D.M. (eds) Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. COSIT 1999. Lecture Notes in Computer Science, vol 1661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48384-5_16
Download citation
DOI: https://doi.org/10.1007/3-540-48384-5_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66365-2
Online ISBN: 978-3-540-48384-7
eBook Packages: Springer Book Archive