Ganter, B. & Wille, R.: Applied lattice theory: formal concept analysis. In: Grätzer, G. (Hrsg.): General lattice theory. 2.. Aufl. to appear

Ganter, B.: Two Basic Algorithms in Concept Analysis. In: Kwuida, L. & Sertkaya, B. (Hrsg.): Formal Concept Analysis. Springer Berlin Heidelberg, 2010 (Lecture Notes in Computer Science 5986), S. 312-340
[Volltext]
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.

Ganter, B.: Two Basic Algorithms in Concept Analysis. In: Kwuida, L. & Sertkaya, B. (Hrsg.): Formal Concept Analysis. Berlin / Heidelberg: Springer, 2010 (Lecture Notes in Computer Science 5986), S. 312-340
[Volltext]

Jäschke, R.; Hotho, A.; Schmitz, C.; Ganter, B. & Stumme, G.: Discovering Shared Conceptualizations in Folksonomies. In: Journal of Web Semantics 6 (2008), Nr. 1, S. 38-53
[Volltext]

Jäschke, R.; Hotho, A.; Schmitz, C.; Ganter, B. & Stumme, G.: Discovering Shared Conceptualizations in Folksonomies. In: Web Semantics: Science, Services and Agents on the World Wide Web 6 (2008), Nr. 1, S. 38-53
[Volltext]
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.

Jäschke, R.; Hotho, A.; Schmitz, C.; Ganter, B. & Stumme, G.: Discovering Shared Conceptualizations in Folksonomies. In: Web Semantics: Science, Services and Agents on the World Wide Web 6 (2008), Nr. 1, S. 38-53
[Volltext]
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.

Jäschke, R.; Hotho, A.; Schmitz, C.; Ganter, B. & Stumme, G.: Discovering shared conceptualizations in folksonomies. In: Web Semant. 6 (2008), Nr. 1, S. 38-53
[Volltext]
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.

Baader, F.; Ganter, B.; Sertkaya, B. & Sattler, U.: Completing description logic knowledge bases using formal concept analysis. Proceedings of the 20th international joint conference on Artifical intelligence. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 2007, S. 230-235
[Volltext]
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.

Ganter, B.: Relational Galois Connections. In: Kuznetsov, S. O. & Schmidt, S. (Hrsg.): Formal Concept Analysis. Springer Berlin Heidelberg, 2007 (Lecture Notes in Computer Science 4390), S. 1-17
[Volltext]
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.

Jäschke, R.; Hotho, A.; Schmitz, C.; Ganter, B. & Stumme, G.: TRIAS - An Algorithm for Mining Iceberg Tri-Lattices. Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06). Hong Kong: IEEE Computer Society, 2006, S. 907-911
[Volltext]

Jäschke, R.; Hotho, A.; Schmitz, C.; Ganter, B. & Stumme, G.: TRIAS - An Algorithm for Mining Iceberg Tri-Lattices. Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06). Hong Kong: IEEE Computer Society, 2006, S. 907-911
[Volltext]
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.

Jäschke, R.; Hotho, A.; Schmitz, C.; Ganter, B. & Stumme, G.: TRIAS - An Algorithm for Mining Iceberg Tri-Lattices. ICDM '06: Proceedings of the Sixth International Conference on Data Mining. Washington, DC, USA: IEEE Computer Society, 2006, S. 907-911
[Volltext]
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.

Ganter, B. & Krauße, R.: Pseudo-models and propositional Horn inference. In: Discrete Applied Mathematics 147 (2005), Nr. 1, S. 43-55
[Volltext]
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.

Ganter, B. & Wille, R.: Formal concept analysis : mathematical foundations. Berlin; New York: Springer, 1999
[Volltext]

Ganter, B. & Wille, R.: Formal Concept Analysis: Mathematical Foundations. Berlin/Heidelberg: Springer, 1999

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.

Ganter, B. & Wille, R.: Formal Concept Analysis: Mathematical Foundations. Berlin/Heidelberg: Springer-Verlag, 1999

Ganter, B. & Kuznetsov, S.: Stepwise construction of the Dedekind-MacNeille completion. In: Mugnier, M.-L. & Chein, M. (Hrsg.): Conceptual Structures: Theory, Tools and Applications. Berlin/Heidelberg: Springer, 1998 (Lecture Notes in Computer Science 1453), S. 295-302
[Volltext]
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.

Ganter, B.: Two basic algorithms in concept analysis. , 1984

Ganter, B.; Poguntke, W. & Wille, R.: Finite sublattices of four-generated modular lattices. In: Algebra Universalis 12 (1981), Nr. 1, S. 160-171
[Volltext]

Ganter, B.; Poguntke, W. & Wille, R.: Finite sublattices of four-generated modular lattices. In: Algebra Univ. 12 (1981), S. 160-171