Abstract
Conceptual patterns can be described by graphs, entailment by graph homomorphism. The mapping of a pattern to its set of instantiations, represented as a table, constitutes one half of a Galois connection. The join operation is the infimum in a complete lattice of tables, and a most descriptive pattern can be assigned to each table by means of a categorial product construction. This construction constitutes the other half of the Galois connection. In this approach, relational structures assume the role of formal contexts in standard Formal Concept Analysis (FCA). Concepts arise as connected components of powers of these relational structures. The ordered set of these concepts may be conceived as a navigation space.
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References
Azmeh, Z., Huchard, M., Napoli, A., Hacene, M.R., Valtchev, P.: Querying relational concept lattices. In: Proc. of the 8th Intl. Conf. on Concept Lattices and their Applications (CLA 2011), pp. 377–392 (2011)
Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational databases. In: Proceedings of the Ninth Annual ACM Symposium on Theory of Computing, STOC 1977, pp. 77–90. ACM, New York (1977)
Ferré, S.: Conceptual Navigation in RDF Graphs with SPARQL-Like Queries. In: Kwuida, L., Sertkaya, B. (eds.) ICFCA 2010. LNCS, vol. 5986, pp. 193–208. Springer, Heidelberg (2010)
Ganter, B., Grigoriev, P.A., Kuznetsov, S.O., Samokhin, M.V.: Concept-Based Data Mining with Scaled Labeled Graphs. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 94–108. Springer, Heidelberg (2004)
Ganter, B., Kuznetsov, S.O.: Pattern Structures and Their Projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129–142. Springer, Heidelberg (2001)
Ganter, B., Wille, R.: Formal concept analysis: mathematical foundations. Springer, Berlin (1999)
Godin, R., Saunders, E., Gecsei, J.: Lattice model of browsable data spaces. Inf. Sci. 40(2), 89–116 (1986)
Wille, R.: Conceptual Graphs and Formal Concept Analysis. In: Lukose, D., Delugach, H., Keeler, M., Searle, L., Sowa, J. (eds.) ICCS 1997. LNCS, vol. 1257, pp. 290–303. Springer, Heidelberg (1997)
Wille, R.: Formal concept analysis and contextual logic. In: Hitzler, P., Schärfe, H. (eds.) Conceptual Structures in Practice, pp. 137–173. Chapman & Hall/CRC (2009)
Wolff, K.E.: Relational Scaling in Relational Semantic Systems. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds.) ICCS 2009. LNCS, vol. 5662, pp. 307–320. Springer, Heidelberg (2009)
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Kötters, J. (2013). Concept Lattices of a Relational Structure. In: Pfeiffer, H.D., Ignatov, D.I., Poelmans, J., Gadiraju, N. (eds) Conceptual Structures for STEM Research and Education. ICCS 2013. Lecture Notes in Computer Science(), vol 7735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35786-2_23
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DOI: https://doi.org/10.1007/978-3-642-35786-2_23
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