Conference articles
Applied lattice theory: formal concept analysis.
In: G. Grätzer, editor,
General lattice theory, edition 2..
to appear.
Bernhard Ganter and Rudolf Wille.
[BibTeX]
Book chapters
Two Basic Algorithms in Concept Analysis.
In:
L. Kwuida and B. Sertkaya, editors,
Formal Concept Analysis, pages 312-340.
Springer Berlin Heidelberg, 2010.
Bernhard Ganter.
[doi]
[abstract]
[BibTeX]
We describe two algorithms for closure systems. The purpose of the first is to produce all closed sets of a given closure operator. The second constructs a minimal family of implications for the ”logic” of a closure system. These algorithms then are applied to problems in concept analysis: Determining all concepts of a given context and describing the dependencies between attributes. The problem of finding all concepts is equivalent, e.g., to finding all maximal complete bipartite subgraphs of a bipartite graph.
Two Basic Algorithms in Concept Analysis.
In:
L. Kwuida and B. Sertkaya, editors,
Formal Concept Analysis, pages 312-340.
Springer, Berlin / Heidelberg, 2010.
Bernhard Ganter.
[doi]
[BibTeX]
Journal articles
Discovering Shared Conceptualizations in Folksonomies.
Journal of Web Semantics, 6(1):38-53, 2008.
Robert Jäschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter and Gerd Stumme.
[doi]
[BibTeX]
Discovering Shared Conceptualizations in Folksonomies.
Web Semantics: Science, Services and Agents on the World Wide Web, 6(1):38-53, 2008.
Robert Jäschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter and Gerd Stumme.
[doi]
[abstract]
[BibTeX]
Social bookmarking tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. Unlike ontologies, shared conceptualizations are not formalized, but rather implicit. We present a new data mining task, the mining of all frequent tri-concepts, together with an efficient algorithm, for discovering these implicit shared conceptualizations. Our approach extends the data mining task of discovering all closed itemsets to three-dimensional data structures to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution. Finally, we show the applicability of our approach on three large real-world examples.
Discovering Shared Conceptualizations in Folksonomies.
Web Semantics: Science, Services and Agents on the World Wide Web, 6(1):38-53, 2008.
Robert Jäschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter and Gerd Stumme.
[doi]
[abstract]
[BibTeX]
Social bookmarking tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. Unlike ontologies, shared conceptualizations are not formalized, but rather implicit. We present a new data mining task, the mining of all frequent tri-concepts, together with an efficient algorithm, for discovering these implicit shared conceptualizations. Our approach extends the data mining task of discovering all closed itemsets to three-dimensional data structures to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution. Finally, we show the applicability of our approach on three large real-world examples.
Conference articles
Completing description logic knowledge bases using formal concept analysis.
In:
Proceedings of the 20th international joint conference on Artifical intelligence, pages 230-235.
Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2007.
Franz Baader, Bernhard Ganter, Baris Sertkaya and Ulrike Sattler.
[doi]
[abstract]
[BibTeX]
We propose an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the knowledge base and by a domain expert. The use of techniques from Formal Concept Analysis ensures that, on the one hand, the interaction with the expert is kept to a minimum, and, on the other hand, we can show that the extended knowledge base is complete in a certain, well-defined sense.
Book chapters
Relational Galois Connections.
In:
S. O. Kuznetsov and S. Schmidt, editors,
Formal Concept Analysis, pages 1-17.
Springer Berlin Heidelberg, 2007.
Bernhard Ganter.
[doi]
[abstract]
[BibTeX]
Galois connections can be defined for lattices and for ordered sets. We discuss a rather wide generalisation, which was introduced by Weiqun Xia and has been reinvented under different names: Relational Galois connections between relations. It turns out that the generalised notion is of importance for the original one and can be utilised, e.g., for computing Galois connections.
Conference articles
TRIAS - An Algorithm for Mining Iceberg Tri-Lattices.
In:
Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06), pages 907-911.
IEEE Computer Society, Hong Kong, 2006.
Robert Jäschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter and Gerd Stumme.
[doi]
[BibTeX]
TRIAS - An Algorithm for Mining Iceberg Tri-Lattices.
In:
Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06), pages 907-911.
IEEE Computer Society, Hong Kong, 2006.
Robert Jäschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter and Gerd Stumme.
[doi]
[abstract]
[BibTeX]
In this paper, we present the foundations for mining frequent tri-concepts, which extend the notion of closed itemsets to three-dimensional data to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution as well as experimental results on a large real-world example.
TRIAS - An Algorithm for Mining Iceberg Tri-Lattices.
In:
ICDM '06: Proceedings of the Sixth International Conference on Data Mining, pages 907-911.
IEEE Computer Society, Washington, DC, USA, 2006.
Robert Jäschke, Andreas Hotho, Christoph Schmitz, Bernhard Ganter and Gerd Stumme.
[doi]
[abstract]
[BibTeX]
In this paper, we present the foundations for mining frequent tri-concepts, which extend the notion of closed itemsets to three-dimensional data to allow for mining folk-sonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution as well as experimental results on a large real-world example.
Journal articles
Pseudo-models and propositional Horn inference.
Discrete Applied Mathematics, 147(1):43-55, 2005.
Bernhard Ganter and Rüdiger Krauße.
[doi]
[abstract]
[BibTeX]
A well-known result is that the inference problem for propositional Horn formulae can be solved in linear time. We show that this remains true even in the presence of arbitrary (static) propositional background knowledge. Our main tool is the notion of a cumulated clause, a slight generalization of the usual clauses in Propositional Logic. We show that each propositional theory has a canonical irredundant base of cumulated clauses, and present an algorithm to compute this base.
Conference articles
Creation and Merging of Ontology Top-Levels.
In: A. de Moor, W. Lex and B. Ganter, editors,
Conceptual Structures for Knowledge Creation and Communication., volume 2746, series LNAI, pages 131-145.
Springer, Heidelberg, 2003.
Bernhard Ganter and Gerd Stumme.
[doi]
[abstract]
[BibTeX]
We provide a new method for systematically structuring the top-down level of ontologies.
It is based on an interactive, top--down knowledge acquisition
process, which assures that the knowledge engineer
considers all possible cases while avoiding redundant acquisition.
The method is suited especially for creating/merging the top
part(s) of the ontologies, where high accuracy is required, and for supporting the merging of two (or more) ontologies on that level.
Miscellaneous
Formal concept analysis : mathematical foundations.
1999.
Bernhard Ganter and Rudolf Wille.
[doi]
[BibTeX]
Formal Concept Analysis: Mathematical Foundations.
1999.
Bernhard Ganter and Rudolf Wille.
[abstract]
[BibTeX]
This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thoroughly and illuminated by means of numerous examples.
Formal Concept Analysis: Mathematical Foundations.
1999.
Bernhard Ganter and Rudolf Wille.
[BibTeX]
Book chapters
Stepwise construction of the Dedekind-MacNeille completion.
In:
M.-L. Mugnier and M. Chein, editors,
Conceptual Structures: Theory, Tools and Applications, pages 295-302.
Springer, Berlin/Heidelberg, 1998.
Bernhard Ganter and Sergei Kuznetsov.
[doi]
[abstract]
[BibTeX]
Lattices are mathematical structures which are frequently used for the representation of data. Several authors have considered the problem of incremental construction of lattices. We show that with a rather general approach, this problem becomes well-structured. We give simple algorithms with satisfactory complexity bounds.
Technical reports
Two basic algorithms in concept analysis.
FB4-Preprint, TH Darmstadt, 1984. Number 831.
Bernhard Ganter.
[BibTeX]
Journal articles
Finite sublattices of four-generated modular lattices.
Algebra Universalis, 12(1):160-171, 1981.
Bernhard Ganter, Werner Poguntke and Rudolf Wille.
[doi]
[BibTeX]
Finite sublattices of four-generated modular lattices.
Algebra Univ., 12:160-171, 1981.
Bernhard Ganter, Werner Poguntke and Rudolf Wille.
[BibTeX]