Probabilistic implication bases in FCA and probabilistic bases of GCIs in

References

• Atserias, Albert, and Jos L. Balcázar. 2015. “Entailment among Probabilistic Implications.” In 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, July 6–10, 2015, 621–632. IEEE Computer Society.
   Google Scholar
• Baader, Franz, Diego Calvanese, Deborah L. McGuinness, Daniele Nardi, Peter F. Patel-Schneider, eds. 2003. The Description Logic Handbook: Theory, Implementation, and Applications. New York: Cambridge University Press.
   Google Scholar
• Baader, Franz, and Felix Distel. 2008. “A Finite Basis for the Set of ∈ℒ-Implications Holding in a Finite Model.” In Formal Concept Analysis, 6th International Conference, ICFCA 2008, Montreal, Canada, February 25–28, 2008, Proceedings, Vol. 4933 of Lecture Notes in Computer Science, edited by Raoul Medina and Sergei A. Obiedkov, 46–61. Springer.
   Google Scholar
• Babin, Mikhail A., and Sergei O. Kuznetsov. 2013. “Computing premises of a minimal cover of functional dependencies is intractable.” Discrete Applied Mathematics 161 (6): 742–749.
   Web of Science ®Google Scholar
• Babin, Mikhail A., and Sergei O. Kuznetsov. 2010. “Recognizing Pseudo-intents is coNP-complete.” In Proceedings of the 7th International Conference on Concept Lattices and Their Applications, Sevilla, Spain, October 19–21, 2010, Vol. 672 of CEUR Workshop Proceedings, edited by Marzena Kryszkiewicz and Sergei A. Obiedkov, 294–301. CEUR-WS.org
   Google Scholar
• Balcázar, Jos L. 2008. “Minimum-Size Bases of Association Rules.” In Machine Learning and Knowledge Discovery in Databases, European Conference, ECML/PKDD 2008, Antwerp, Belgium, September 15–19, 2008. Proceedings, Part I, Vol. 5211 of Lecture Notes in Computer Science, edited by Walter Daelemans, Bart Goethals and Katharina Morik, 86–101. Springer.
   Google Scholar
• Bazhanov, Konstantin, and Sergei A. Obiedkov. 2014. “Optimizations in Computing the Duquenne-Guigues Basis of Implications”.” Annals of Mathematics and Artificial Intelligence 70 (1–2): 5–24.
   Web of Science ®Google Scholar
• Beeri, Catriel, and Philip A. Bernstein. 1979. “Computational Problems Related to the Design of Normal Form Relational Schemas.” ACM Transactions on Database Systems 4 (1): 30–59.
   Google Scholar
• Borchmann, Daniel. 2014. “Learning Terminological Knowledge with High Confidence from Erroneous Data.” PhD thesis. Dresden, Germany: Technische Universität Dresden.
   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
• Demin, Alexander V., DenisK Ponomaryov, and Evgenii Vityaev. 2011. “Probabilistic Concepts in Formal Contexts.” In Perspectives of Systems Informatics -- 8th International Andrei Ershov Memorial Conference, PSI 2011, Novosibirsk, Russia, June 27-July 1, 2011, Revised Selected Papers, Vol. 7162 of Lecture Notes in Computer Science, edited by Edmund M. Clarke, Irina Virbitskaite and Andrei Voronkov, 394–410. Springer.
   Google Scholar
• Distel, Felix. 2011. “Learning Description Logic Knowledge Bases from Data using Methods from Formal Concept Analysis.” Ph.D. thesis, Technische Universität Dresden.
   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 Lonard Kwuida and Barf Sertkaya, 124–137. Springer.
   Google Scholar
• Distel, Felix, and Barşf Sertkaya. 2011. “On the Complexity of Enumerating Pseudo-intents.” Discrete Applied Mathematics 159 (6): 450–466.
   Web of Science ®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. 5986 of Lecture Notes in Computer Science, edited by Lonard Kwuida and Bar Sertkaya, 312–340. Springer.
   Google Scholar
• Ganter, Bernhard, and Rudolf Wille. 1999. Formal Concept Analysis -- Mathematical Foundations. Berlin: 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. 2015a. “Axiomatization of General Concept Inclusions in Probabilistic Description Logics.” In KI 2015: Advances in Artificial Intelligence -- 38th Annual German Conference on AI, Dresden, Germany, September 21–25, 2015, Proceedings, Vol. 9324 of Lecture Notes in Computer Science, edited by Steffen Hölldobler,, Markus Krötzsch, Rafael Peñaloza and Sebastian Rudolph, 124–136. Springer.
   Google Scholar
• Kriegel, Francesco. 2015b. “NextClosures -- Parallel Exploration of Constrained Closure Operators LTCS-Report 15–01.” Chair for Automata Theory, Technische Universität Dresden.
   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
• Kriegel, Francesco. 2016a. “NextClosures with Constraints.” In Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications, Moscow, Russia, July 18–22, 2016, Vol. 1624 of CEUR Workshop Proceedings, edited by Marianne Huchard and Sergei O. Kuznetsov, 231–243. 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
• Kuznetsov, Sergei O. 2001. “On Computing the Size of a Lattice and Related Decision Problems.” Order 18 (4): 313–321.
   Web of Science ®Google Scholar
• Kuznetsov, Sergei O. 2004. “On the Intractability of Computing the Duquenne--Guigues Base.”J. UCS 10 (8): 927–933.
   Web of Science ®Google Scholar
• Kuznetsov, Sergei O., and Sergei A. Obiedkov. 2008. “Some Decision and Counting Problems of the Duquenne--Guigues Basis of Implications.” Discrete Applied Mathematics 156 (11): 1994–2003.
   Web of Science ®Google Scholar
• Kuznetsov, Sergei O., and Sergei A. Obiedkov. 2006. “Counting Pseudo-intents and \#P-completeness.” In Formal Concept Analysis, 4th International Conference, ICFCA 2006, Dresden, Germany, February 13–17, 2006, Proceedings, Vol. 3874 of Lecture Notes in Computer Science, edited by Rokia Missaoui and Jrg Schmid, 306–308. Springer.
   Google Scholar
• Lutz, Carsten, and Lutz Schröder. 2010. “Probabilistic Description Logics for Subjective Uncertainty.” In Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference, KR 2010, Toronto, Ontario, Canada, May 9–13, 2010, edited by Fangzhen Lin, Ulrike Sattler and Miroslaw Truszczynski, AAAI Press.
   Google Scholar
• Luxenburger, Michael. 1993. “Implikationen, Abhängigkeiten und Galois Abbildungen.” PhD thesis, Darmstadt, Germany: Technische Hochschule Darmstadt.
   Google Scholar
• Maier, David. 1983. The Theory of Relational Databases. Rockville, MD: Computer Science Press.
   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
• Sertkaya, Barf. 2009a. “Some Computational Problems Related to Pseudo-intents.” In Formal Concept Analysis, 7th International Conference, ICFCA 2009, Darmstadt, Germany, May 21–24, 2009, Proceedings, Vol. 5548 of Lecture Notes in Computer Science edited by Sbastien Ferré and Sebastian Rudolph, 130–145. Springer.
   Google Scholar
• Sertkaya, Barf. 2009b. “Towards the Complexity of Recognizing Pseudo-intents.” In Conceptual Structures: Leveraging Semantic Technologies, 17th International Conference on Conceptual Structures, ICCS 2009, Moscow, Russia, July 26–31, 2009, Proceedings, Vol. 5662 of Lecture Notes in Computer Science edited by Sebastian Rudolph, Frithjof Dau and Sergei O. Kuznetsov, 284–292. Springer.
   Google Scholar
• Stumme, Gerd. 1996. “Attribute Exploration with Background Implications and Exceptions.” In Studies in Classification, Data Analysis, and Knowledge Organization, 457–469. Berlin, Heidelberg: Springer.
   Google Scholar
• Wild, Marcel. 1995. “Computations with Finite Closure Systems and Implications.” In Computing and Combinatorics, First Annual International Conference, COCOON ’95, Xi’an, China, August 24–26, 1995, Proceedings, Vol. 959 of Lecture Notes in Computer Science edited by Ding- Zhu Du, and Ming Li, 111–120. Springer.
   Google Scholar
• Wille, Rudolf. 1982. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts, 445–470. Dordrecht: Springer Netherlands.
   Google Scholar