Abstract
The present paper is concerned with Rough Set Theory (RST) and Similarity Coverage Model (SCM) of category-based induction. It redefines basic concepts of RST in the light of SCM, and explains how RST may be seen as an elegant formal model of inductive reasoning. Furthermore, following SCM, we enrich RST by the concept of an ontology defined as a subset of the family of all definable sets. The paper also presents a model of inductive reasoning which is driven by recent works on RST and nearness-type structures. We show how approximation spaces can be characterised in terms of non-Archimedean nearness spaces.
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
Atran, S.: Classifying nature across cultures. In: Osherson, D., Smith, E. (eds.) An Invitation to Cognitive Science. Thinking, pp. 131–174. MIT Press, Cambridge, MA (1995)
Deses, D., Lowen-Colebunders, E.: On completeness in a non-Archimedean setting, via firm reflections. Bulletin of the Belgian Mathematical Society, Special volume: p-adic numbers in number theory, analytic geometry and functional analysis, pp. 49–61(2002)
Deses, D.: Completeness and zero-dimensionality arising from the duality between closures and lattices. PhD. Thesis, Free University of Brussels (2003) http://homepages.vub.ac.be/~diddesen/phdthesis.pdf
Gomolińska, A.: Approximation spaces based on similarity and dissimilarity. In: Lindemann, G., Schlingloff, H., Burkhard, H., Czaja, L., Penczek, W., Salwicki, A., Skowron, A., Suraj, Z. (eds.) Concurrency, Specification and Programming CS&P’, Informatik-Berichte 206, Berlin 2006, pp. 446–457 (2006)
Heit, E.: Properties of inductive reasoning. Psychonomic Bulletin & Review 7, 569–592 (2000)
Osherson, D.N., Smith, E.E., Wilkie, O., Lopez, A., Shafir, E.: Category-based induction. Psychological Review 97(2), 185–200 (1990)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston (1991)
Peters, J., Skowron, A., Stepaniuk, J.: Nearness in approximation spaces. In: Lindemann, G., Schlingloff, H., Burkhard, H., Czaja, L., Penczek, W., Salwicki, A., Skowron, A., Suraj, Z. (eds.): Concurrency, Specification and Programming CS&P’, Informatik-Berichte 206, Berlin 2006, pp. 434–445 (2006)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Sloman, S.A.: Feature-based induction. Cognitive Psychology 25, 231–280 (1993)
Wolski, M.: Similarity as Nearness: Information Quanta, Approximation Spaces and Nearness Structures. In: Lindemann, G., Schlingloff, H., Burkhard, H., Czaja, L., Penczek, W., Salwicki, A., Skowron, A., Suraj, Z. (eds.): Concurrency, Specification and Programming CS&P’2006, Informatik-Berichte 206, Berlin 2006, pp. 423–433 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wolski, M. (2007). Category-Based Rough Induction. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds) Rough Sets and Intelligent Systems Paradigms. RSEISP 2007. Lecture Notes in Computer Science(), vol 4585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73451-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-73451-2_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73450-5
Online ISBN: 978-3-540-73451-2
eBook Packages: Computer ScienceComputer Science (R0)