Abstract
The notions of 2-precontact and 2-contact spaces as well as of extensional (and other kinds) 3-precontact and 3-contact spaces are introduced. Using them, new representation theorems for precontact and contact algebras (satisfying some additional axioms) are proved. They incorporate and strengthen both the discrete and topological representation theorems from [3, 1, 2, 4, 10]. It is shown that there are bijective correspondences between such kinds of algebras and such kinds of spaces. In particular, such a bijective correspondence for the RCC systems of [8] is obtained, strengthening in this way the previous representation theorems from [4, 1].
This paper was supported by the project NIP-123 “Applied Logics and Topological Structures” of the Bulgarian Ministry of Education and Science.
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
Dimov, G., Vakarelov, D.: Contact Algebras and Region-based Theory of Space: A Proximity Approach - I (submitted, 2004)
Dimov, G., Vakarelov, D.: Contact Algebras and Region-based Theory of Space: A Proximity Approach - II (submitted, 2004)
Düntsch, I., Vakarelov, D.: Region-based theory of discrete spaces: A proximity approach. In: Nadif, M., Napoli, A., SanJuan, E., Sigayret, A. (eds.) Proceedings of Fourth International Conference Journées de l’informatique Messine, Metz, France, pp. 123–129 (2003) (to appear in Discrete Applied Mathematics)
Düntsch, I., Winter, M.: A Representation theorem for Boolean Contact Algebras (2003) (to appear in Theoretical Computer Science)
Engelking, R.: General Topology. PWN, Warszawa (1977)
Galton, A.: The mereotopology of discrete spaces. In: Freksa, C., Mark, D.M. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 251–266. Springer, Heidelberg (1999)
Li, S., Ying, M.: Generalized Connection Calculus. Artificial Intelligence (in print, 2004)
Randell, D., Cui, Z., Cohn, A.G.: A Spatial Logic based on Regions and Connection. In: Nebel, B., Swartout, W., Rich, C. (eds.) Proc. of the 3rd International Conference On Principles of Knowledge Representation and Reasoning, Cambridge, MA, pp. 165–176. Morgan Caufmann, San Francisco (1992)
Thron, W.: Proximity structures and grills. Math. Ann. 206, 35–62 (1973)
Vakarelov, D., Dimov, G., Düntsch, I., Bennett, B.: A proximity approach to some region-based theory of space. Journal of applied non-classical logics 12(3-4), 527–559 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dimov, G., Vakarelov, D. (2006). Topological Representation of Precontact Algebras. In: MacCaull, W., Winter, M., Düntsch, I. (eds) Relational Methods in Computer Science. RelMiCS 2005. Lecture Notes in Computer Science, vol 3929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734673_1
Download citation
DOI: https://doi.org/10.1007/11734673_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33339-5
Online ISBN: 978-3-540-33340-1
eBook Packages: Computer ScienceComputer Science (R0)