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A Formal Context for Closures of Acyclic Hypergraphs

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11511))

Abstract

Database constraints in the relational database model (RDBM) can be viewed as a set of rules that apply to a dataset, or as a set of axioms that can generate a (closed) set of those constraints. In this paper, we use Formal Concept Analysis to characterize the axioms of Acyclic Hypergraphs (in the RDBM they are called Acyclic Join Dependencies). This present paper complements and generalizes previous work on FCA and databases constraints.

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References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)

    MATH  Google Scholar 

  2. Baixeries, J.: A formal concept analysis framework to model functional dependencies. In: Mathematical Methods for Learning (2004)

    Google Scholar 

  3. Baixeries, J.: Lattice characterization of Armstrong and symmetric dependencies (Ph.D. thesis). Universitat Politècnica de Catalunya (2007)

    Google Scholar 

  4. Baixeries, J.: A formal context for symmetric dependencies. In: Medina, R., Obiedkov, S. (eds.) ICFCA 2008. LNCS (LNAI), vol. 4933, pp. 90–105. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78137-0_7

    Chapter  MATH  Google Scholar 

  5. Baixeries, J.: A new formal context for symmetric dependencies (2011)

    Google Scholar 

  6. Baixeries, J.: A formal context for acyclic join dependencies. In: Kryszkiewicz, M., Appice, A., Ślęzak, D., Rybinski, H., Skowron, A., Raś, Z.W. (eds.) ISMIS 2017. LNCS (LNAI), vol. 10352, pp. 563–572. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60438-1_55

    Chapter  Google Scholar 

  7. Baixeries, J., Balcázar, J.L.: Discrete deterministic data mining as knowledge compilation. In: Proceedings of Workshop on Discrete Mathematics and Data Mining - SIAM (2003)

    Google Scholar 

  8. Baixeries, J., Balcázar, J.L.: Characterization and Armstrong relations for degenerate multivalued dependencies using formal concept analysis. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 162–175. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32262-7_11

    Chapter  MATH  Google Scholar 

  9. Baixeries, J., Balcázar, J.L.: A lattice representation of relations, multivalued dependencies and Armstrong relations. In: ICCS, pp. 13–26 (2005)

    Google Scholar 

  10. Baixeries, J., Codocedo, V., Kaytoue, M., Napoli, A.: Characterizing approximate-matching dependencies in formal concept analysis with pattern structures. Discrete Appl. Math. 249, 18–27 (2018). Concept Lattices and Applications: Recent Advances and New Opportunities

    Google Scholar 

  11. Baixeries, J., Kaytoue, M., Napoli, A.: Computing functional dependencies with pattern structures. In: Szathmary, L., Priss, U. (eds.) CLA, volume 972 of CEUR Workshop Proceedings, pp. 175–186. CEUR-WS.org (2012)

    Google Scholar 

  12. Baixeries, J., Kaytoue, M., Napoli, A.: Computing similarity dependencies with pattern structures. In: Ojeda-Aciego, M., Outrata, J. (eds.) CLA, volume 1062 of CEUR Workshop Proceedings, pp. 33–44. CEUR-WS.org (2013)

    Google Scholar 

  13. Baixeries, J., Kaytoue, M., Napoli, A.: Characterizing functional dependencies in formal concept analysis with pattern structures. Ann. Math. Artif. Intell. 72(1–2), 129–149 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. J. ACM 30(3), 479–513 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  15. Beeri, C., Vardi, M.Y.: Formal systems for join dependencies. Theor. Comput. Sci. 38, 99–116 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bělohlávek, R., Vychodil, V.: Data tables with similarity relations: functional dependencies, complete rules and non-redundant bases. In: Li Lee, M., Tan, K.-L., Wuwongse, V. (eds.) DASFAA 2006. LNCS, vol. 3882, pp. 644–658. Springer, Heidelberg (2006). https://doi.org/10.1007/11733836_45

    Chapter  Google Scholar 

  17. Berge, C.: Hypergraphs: Combinatorics of Finite Sets, volume 45 of North-Holland Mathematical Library. North-Holland, Amsterdam (1989)

    Google Scholar 

  18. Bohannon, P., Fan, W., Geerts, F., Jia, X., Kementsietsidis, A.: Conditional functional dependencies for data cleaning. In: ICDE, pp. 746–755 (2007)

    Google Scholar 

  19. Brault-Baron, J.: Hypergraph acyclicity revisited. ACM Comput. Surv. 49, 03 (2014)

    Google Scholar 

  20. Caspard, N., Monjardet, B.: The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey. Discrete Appl. Math. 127(2), 241–269 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  21. Codd, E.F.: Further normalization of the data base relational model. IBM Research Report, San Jose, California, RJ909 (1971)

    Google Scholar 

  22. Day, A.: The lattice theory of functionnal dependencies and normal decompositions. Int. J. Algebr. Comput. 02(04), 409–431 (1992)

    Article  MATH  Google Scholar 

  23. Day, A.: A lattice interpretation of database dependencies. In: Semantics of Programming Languages and Model Theory, pp. 305–325. Gordon and Breach Science Publishers Inc, Newark (1993)

    Google Scholar 

  24. Demetrovics, J., Hencsey, G., Libkin, L., Muchnik, I.B.: Normal form relation schemes: a new characterization. Acta Cybern. 10(3), 141–153 (1992)

    MathSciNet  MATH  Google Scholar 

  25. Demetrovics, J., Huy, N.: Representation of closure for functional, multivalued and join dependencies. Comput. Artif. Intell. 11(2), 143–154 (1992)

    MATH  Google Scholar 

  26. Demetrovics, J., Libkin, L., Muchnik, I.B.: Functional dependencies in relational databases: a lattice point of view. Discrete Appl. Math. 40(2), 155–185 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Berlin (1999). https://doi.org/10.1007/978-3-642-59830-2

    Book  MATH  Google Scholar 

  28. Gyssens, M.: On the complexity of join dependencies. ACM Trans. Database Syst. 11(1), 81–108 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  29. Kuznetsov, S.O.: Machine learning on the basis of formal concept analysis. Autom. Remote Control 62(10), 1543–1564 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  30. Lopes, S., Petit, J.-M., Lakhal, L.: Functional and approximate dependency mining: database and fca points of view. J. Exp. Theor. Artif. Intell. 14(2–3), 93–114 (2002)

    Article  MATH  Google Scholar 

  31. Maier, D.: The Theory of Relational Databases. Computer Science Press, Rockville (1983)

    MATH  Google Scholar 

  32. Malvestuto, F.: A complete axiomatization of full acyclic join dependencies. Inf. Process. Lett. 68(3), 133–139 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  33. Ullman, J.: Principles of Database Systems and Knowledge-Based Systems, vol. 1–2. Computer Science Press, Rockville (1989)

    Google Scholar 

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Acknowledgments

This research was supported by the recognition of 2017SGR-856 (MACDA) from AGAUR (Generalitat de Catalunya), and the grant TIN2017-89244-R from MINECO (Ministerio de Economía y Competitividad).

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Correspondence to Jaume Baixeries .

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Baixeries, J. (2019). A Formal Context for Closures of Acyclic Hypergraphs. In: Cristea, D., Le Ber, F., Sertkaya, B. (eds) Formal Concept Analysis. ICFCA 2019. Lecture Notes in Computer Science(), vol 11511. Springer, Cham. https://doi.org/10.1007/978-3-030-21462-3_17

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  • DOI: https://doi.org/10.1007/978-3-030-21462-3_17

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