Abstract
We propose the generalization of the notion bond between two formal contexts to the case of n formal contexts. The first properties of the n-ary bonds are given, together with a method for building n-ary bonds. This construction enables to formalize some inference rules within the research topic of building a sequent calculus for formal contexts.
Ondrej Krídlo—Partially supported by grants VEGA 1/0073/15 and APVV-15-0091.
Manuel Ojeda-Aciego—Partially supported by Spanish Ministry of Science project TIN2015-70266-C2-1-P, co-funded by the European Regional Development Fund (ERDF).
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References
Bělohlávek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic Publishers, Dordrecht (2002)
Cellier, P., Ferré, S., Ducassé, M., Charnois, T.: Partial orders and logical concept analysis to explore patterns extracted by data mining. Lecture Notes in Artificial Intelligence, vol. 6828, pp. 77–90. Springer, Berlin (2011)
Ganter, B., Wille, R.: Contextual attribute logic. Lecture Notes in Computer Science, vol. 1640, pp. 377–388. Springer, Berlin (1999)
Hitzler, P., Krötzsch, M.: Querying formal contexts with answer set programs. Lecture Notes in Computer Science, vol. 4068, pp. 260–273. Springer, Berlin (2006)
Hitzler, P., Zhang, G.-Q.: A cartesian closed category of approximable concept structures. Lecture Notes in Artificial Intelligence, vol. 3127, pp. 170–185. Springer, Berlin (2004)
Krídlo, O., Krajči, S., Ojeda-Aciego, M.: The category of \(L\)-Chu correspondences and the structure of \(L\)-bonds. Fundamenta Informaticae 115(4), 297–325 (2012)
Krídlo, O., Ojeda-Aciego, M.: Towards a sequent calculus for formal contexts. In: Proceedings of the 5th International Workshop What Can FCA Do for Artificial Intelligence? FCA4AI, CEUR-WS, vol. 1703, pp. 17–24 (2016)
Krötzsch, M., Hitzler, P., Zhang, G.-Q.: Morphisms in context. Lecture Notes in Computer Science, vol. 3596, pp. 223–237. Springer, Berlin (2005)
Mac Lane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics, vol. 5. Springer, Berlin (1971)
Ridoux, O., Ferré, S.: Introduction to logical information systems. Inf. Process. Manag. 40, 383–419 (2004)
Acknowledgements
Partially supported by the Slovak Research and Development Agency contract No. APVV-15-0091, University Science Park TECHNICOM for Innovation Applications Supported by Knowledge Technology, ITMS: 26220220182 and II. Phase, ITMS2014+: 313011D232, supported by the ERDF.
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Krídlo, O., Ojeda-Aciego, M. (2019). On the n-ary Generalization of Dual Bonds. In: Kóczy, L., Medina-Moreno, J., Ramírez-Poussa, E. (eds) Interactions Between Computational Intelligence and Mathematics Part 2. Studies in Computational Intelligence, vol 794. Springer, Cham. https://doi.org/10.1007/978-3-030-01632-6_4
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DOI: https://doi.org/10.1007/978-3-030-01632-6_4
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