Abstract
The aim of this paper is to contribute to Data Analysis by clarifying how concept graphs may be derived from data tables. First it is shown how, by the method of relational scaling, a many-valued data context can be transformed into a power context family. Then it is proved that the concept graphs of a power context family form a lattice which can be described as a subdirect product of specific intervals of the concept lattices of the power context family (each extended by a new top-element). How this may become practical is demonstrated using a data table about the domestic flights in Austria. Finally, the lattice of syntactic concept graphs over an alphabet of object, concept, and relation names is determined and related to the lattices of concept graphs of the power context families which are semantic models of the given contextual syntax.
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.
Similar content being viewed by others
References
B. Ganter, R. Wille: Conceptual scaling. In: F. S. Roberts (ed.): Applications of Combinatorics and Graph Theory to the Biological and Social Sciences. Springer, Berlin-Heidelberg-New York 1989, 139–167.
B. Ganter, R. Wille: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin-Heidelberg-New York 1999.
I. Kant: Logic. Dover, New York 1988.
OAG Pocket Flight Guide-Europe/Africa/Middle East. Reed Elsevier, July 1998.
S. Prediger: Simple concept graphs: a logic approach. In: M.-L. Mugnier. M. Chein (eds.): Conceptual Structures: Theory, Tools and Applications. Springer, Berlin-Heidelberg-New York 1998, 225–239.
S. Prediger: Kontextuelle Urteilslogik mit Begriffsgraphen. Ein Beitrag zur Restrukturierung der mathematischen Logik. Dissertation, Shaker Verlag, Aachen 1998.
J. F. Sowa: Conceptual structures: information processing in mind and machine. Addison-Wesley, Reading 1984.
J. F. Sowa: Conceptual graphs summary. In: T. E. Nagle, J. A. Nagle, L. L. Gerholz, P. W. Eklund (eds.): Conceptual Structures: Current Research and Practice. Ellis Horwood 1992, 3–51.
F. Vogt, R. Wille: TOSCANA-a graphical tool for analyzing and exploring data. In: R. Tamassia, I. G. Tollis (eds.): Graph Drawing. LNCS 894. Springer, Berlin-Heidelberg-New York 1995, 226–233.
R. Wille: Restructuring lattice theory: an approach based on hierarchies of concepts. In: I. Rival (ed.): Ordered sets. Reidel, Dordrecht, Boston 1982, 445–470.
R. Wille: Conceptual Graphs and Formal Concept Analysis. In: D. Lukose, H. Delugach, M. Keeler, L. Searle, J. Sowa (eds.): Conceptual Structures: Fulfilling Peirce’s Dream. Springer, Berlin-Heidelberg-New York 1997, 290–303.
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
Prediger, S., Wille, R. (1999). The Lattice of Concept Graphs of a Relationally Scaled Context. In: Tepfenhart, W.M., Cyre, W. (eds) Conceptual Structures: Standards and Practices. ICCS 1999. Lecture Notes in Computer Science(), vol 1640. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48659-3_25
Download citation
DOI: https://doi.org/10.1007/3-540-48659-3_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66223-5
Online ISBN: 978-3-540-48659-6
eBook Packages: Springer Book Archive