NextClosures: parallel computation of the canonical base with background knowledge

References

• Belohlávek, Radim, and Vilém Vychodil. 2006. “Formal Concept Analysis with Constraints by Closure Operators.” In Conceptual Structures: Inspiration and Application, 14th International Conference on Conceptual Structures, ICCS 2006, Aalborg, Denmark, July 16--21, 2006, Proceedings, Vol. 4068 of Lecture Notes in Computer Science, edited by Henrik Schärfe, Pascal Hitzler, and Peter Øhrstrøm, 131–143. Springer.
   Google Scholar
• Belohlávek, Radim, and Vilém Vychodil. 2013. “Closure-based Constraints in Formal Concept Analysis.” Discrete Applied Mathematics 161 (13–14): 1894–1911.
   Web of Science ®Google Scholar
• Borchmann, Daniel, Felix Distel, and Francesco Kriegel. 2016. “Axiomatisation of General Concept Inclusions from Finite Interpretations.” Journal of Applied Non-Classical Logics 26 (1): 1–46.
   Google Scholar
• Distel, Felix. 2010. “Hardness of Enumerating Pseudo-intents in the Lectic Order.” In Formal Concept Analysis, 8th International Conference, ICFCA 2010, Agadir, Morocco, March 15--18,2010. Proceedings, Vol. 5986 of Lecture Notes in Computer Science, edited by Léonard Kwuida and Baríş Sertkaya, 124–137. Springer.
   Google Scholar
• Distel, Felix. 2011. “Learning Description Logic Knowledge Bases from Data using Methods from Formal Concept Analysis.” PhD thesis, Technische Universität Dresden.
   Google Scholar
• Distel, Felix, and Baríş Sertkaya. 2011. “On the Complexity of Enumerating Pseudo-intents.” Discrete Applied Mathematics 159 (6): 450–466.
   Web of Science ®Google Scholar
• FCA Data Repository. Office since 2013. http://www.fcarepository.com.
   Google Scholar
• Fu, Huaiguo, and Engelbert Mephu Nguifo. 2004. “A Parallel Algorithm to Generate Formal Concepts for Large Data.” In Concept Lattices, Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23--26, 2004, Proceedings, Vol. 2961 of Lecture Notes in Computer Science, edited by Peter W. Eklund, 394–401.Springer.
   Google Scholar
• Ganter, Bernhard. 1984. Two Basic Algorithms in Concept Analysis. FB4-Preprint 831. Darmstadt, Germany: Technische Hochschule Darmstadt.
   Google Scholar
• Ganter, Bernhard. 1999. “Attribute Exploration with Background Knowledge.” Theoretical Computer Science 217 (2): 215–233.
   Web of Science ®Google Scholar
• Ganter, Bernhard. 2010. “Two Basic Algorithms in Concept Analysis.” In Formal Concept Analysis, 8th International Conference, ICFCA 2010, Agadir, Morocco, March 15--18, 2010. Proceedings, Vol. 5968 of Lecture Notes in Computer Science, edited by Léonard Kwuida and Baríş Sertkaya, 312–340. Springer.
   Google Scholar
• Ganter, Bernhard, and Sergei A. Obiedkov. 2016. Conceptual Exploration. Berlin/Heidelberg: Springer.
   Google Scholar
• Ganter, Bernhard, and Rudolf Wille. 1999. Formal Concept Analysis -- Mathematical Foundations. Berlin/Heidelberg: Springer.
   Google Scholar
• Guigues, Jean-Luc, and Vincent Duquenne. 1986. “Famille minimale d’implications informatives résultant d’un tableau de données binaires.” Mathématiques et Sciences Humaines 95: 5–18.
   Google Scholar
• Kriegel, Francesco. 2010--2017. “Concept Explorer FX.” Software for Formal Concept Analysis with Description Logic Extensions. https://github.com/francesco-kriegel/conexp-fx.
   Google Scholar
• Kriegel, Francesco. 2015. NextClosures -- Parallel Exploration of Constrained Closure Operators. LTCS-Report 15-01. Chair for Automata Theory, Technische Universität Dresden.
   Google Scholar
• Kriegel, Francesco. 2016a. “Axiomatization of General Concept Inclusions from Streams of Interpretations with Optional Error Tolerance.” In Proceedings of the 5th International Workshop “What can FCA do for Artificial Intelligence”? Co-located with the European Conference on Artificial Intelligence, FCA4AI@ECAI 2016, The Hague, The Netherlands, August 30, 2016, Vol. 1703 of CEUR Workshop Proceedings, edited by Sergei O. Kuznetsov, Amedeo Napoli and Sebastian Rudolph, 9–16. CEUR-WS.org.
   Google Scholar
• Kriegel, Francesco. 2016b. “Parallel Attribute Exploration.” In Graph-based Representation and Reasoning -- 22nd International Conference on Conceptual Structures, ICCS 2016, Annecy, France, July 5--7, 2016, Proceedings, Vol. 9717 of Lecture Notes in Computer Science, edited by Ollivier Haemmerlé, Gem Stapleton and Catherine Faron-Zucker, 91–106. Springer.
   Google Scholar
• Kriegel, Francesco, and Daniel Borchmann. 2015. “NextClosures: Parallel Computation of the Canonical Base.” In Proceedings of the Twelfth International Conference on Concept Lattices and their Applications, Clermont-Ferrand, France, October 13--16, 2015, Vol. 1466 of CEUR Workshop Proceedings, edited by Sadok Ben Yahia and Jan Konecny, 181–192. CEUR-WS.org.
   Google Scholar
• Kuznetsov, Sergei O. 2004. “On the Intractability of Computing the Duquenne-Guigues Base.” Journal of Universal Computer Science 10 (8): 927–933.
   Web of Science ®Google Scholar
• Lindig, Christian. 2000. “Fast Concept Analysis.” In Working with Conceptual Structures -- Contributions to ICCS 2000, edited by Gerhard Stumme, 152–161. Aachen, Germany: Shaker Verlag. Supplemental Proceedings to Conceptual Structures: Logical, Linguistic, and Computational Issues, 8th International Conference on Conceptual Structures, ICCS 2000, Darmstadt, Germany, August 14--18, 2000.
   Google Scholar
• Obiedkov, Sergei A., and Vincent Duquenne. 2007. “Attribute-incremental Construction of the Canonical Implication Basis.” Annals of Mathematics and Artificial Intelligence 49 (1–4): 77–99.
   Web of Science ®Google Scholar
• Stumme, Gerd. 1996. “Attribute Exploration with Background Implications and Exceptions.” Studies in Classification, Data Analysis, and Knowledge Organization, 457–469. Berlin: Springer.
   Google Scholar
• Vychodil, Vilém, Petr Krajča, and Jan Outrata. 2008. “Parallel Recursive Algorithm for FCA.” In Proceedings of the 6th International Conference on Concept Lattices and their Applications, edited by Radim Bělohlávek and Sergei O. Kuznetsov, 71–82. Olomouc: Palacký University.
   Google Scholar
• Wille, Rudolf. 1982. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts, 445–470. Dordrecht: Springer Netherlands.
   Google Scholar