Abstract
This paper offers an approach of developing an order- theoretic structure theory of two-dimensional convex continuum structures. The chosen approach is based on convex planar continua and their subcontinua as primitive notions. In a first step convex planar continua are mathematized and represented by ordered sets. In a second step ‘points’ are deduced as limits of continua by methods of Formal Concept Analysis. The convex continuum structures extended by those points give rise to complete atomistic lattices the atoms of which are just the smallest points. Further research is planned to extend the approach of this paper to higher dimensional continuum structures.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aristoteles Werke in deutscher Übersetzung. Bd. 11: Physikvorlesung. 5. Aufl. Akademie Verlag, Berlin (1995)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Hartung, G.: A topological representation of lattices. Algebra Universalis 29, 273–299 (1992)
Laugwitz, D.: Zahlen und Kontinuum. B.I.-Wissenschaftsverlag, Mannheim (1986)
Piaget, J.: La formation du symbole chez l’enfant-imitation, jeu et rêve - Image et représentation. Delachaux et Niestlé S.A., Neuchâtel (1959)
Stahl, J., Wille, R.: Preconcepts and set representations of contexts. In: Gaul, W., Schader, M. (eds.) Classification as a tool of research, pp. 431–438. North-Holland, Amsterdam (1986)
Urquhart, A.: A topological representation theory for lattices. Algebra Universalis 8, 45–58 (1978)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Reidel, Dordrecht (1982)
Wille, R.: Formal Concept Analysis of one-dimensional continuum structures. Algebra Universalis 59, 197–208 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wille, R. (2010). Formal Concept Analysis of Two-Dimensional Convex Continuum Structures. In: Kwuida, L., Sertkaya, B. (eds) Formal Concept Analysis. ICFCA 2010. Lecture Notes in Computer Science(), vol 5986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11928-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-11928-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11927-9
Online ISBN: 978-3-642-11928-6
eBook Packages: Computer ScienceComputer Science (R0)