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Generalised N-ary Relations and Allegories

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Relational and Algebraic Methods in Computer Science (RAMICS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9348))

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Abstract

Allegories abstract useful features of the enriched category of sets and binary relations. N-ary relations can be easily defined in any allegory with relational products as binary relations between appropriate product objects. Unfortunately, in many applications (especially those related to databases) such an indirect way of thinking about N-ary relations is somewhat awkward. In this paper we develop a formalism for allegorical generalisations of N-ary relations particularly well suited for database applications.

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References

  1. Data Mining Extensions (DMX) Reference, https://msdn.microsoft.com/en-us/library/ms132058.aspx

  2. Barr, M., Wells, C.: Category theory for computing science. Prentice-Hall International Series in Computer Science. Prentice Hall (1995)

    Google Scholar 

  3. Berghammer, R., Haeberer, A., Schmidt, G., Veloso, P.: Comparing two different approaches to products in abstract relation algebra. In: Algebraic Methodology and Software Technology (AMAST 1993), pp. 167–176. Springer (1994)

    Google Scholar 

  4. Brown, C., Hutton, G.: Categories, allegories and circuit design. In: Proceedings of the Symposium on Logic in Computer Science, LICS 1994, pp. 372–381. IEEE (1994)

    Google Scholar 

  5. Brown, C., Jeffrey, A.: Allegories of circuits. In: Matiyasevich, Y.V., Nerode, A. (eds.) LFCS 1994. LNCS, vol. 813, pp. 56–68. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  6. Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13(6), 377–387 (1970), http://doi.acm.org/10.1145/362384.362685

    Article  MATH  Google Scholar 

  7. Davey, B., Priestley, H.: Introduction to Lattices and Order. Cambridge mathematical text books. Cambridge University Press (2002)

    Google Scholar 

  8. Desharnais, J.: Monomorphic characterization of n-ary direct products. Inf. Sci. 119(3-4), 275–288 (1999), http://dx.doi.org/10.1016/S0020-02559900020-1

  9. Freyd, P., Scedrov, A.: Categories, Allegories. North-Holland Mathematical Library. Elsevier Science (1990)

    Google Scholar 

  10. Givant, S.: The calculus of relations as a foundation for mathematics. Journal of Automated Reasoning 37(4), 277–322 (2006), http://dx.doi.org/10.1007/s10817-006-9062-x

    Article  MathSciNet  MATH  Google Scholar 

  11. Schmidt, G., Ströhlein, T.: Relations and graphs. Springer, Heidelberg (1993)

    Book  MATH  Google Scholar 

  12. Schmidt, G., Winter, M.: Relational mathematics continued. arXiv:1403.6957 (2014)

    Google Scholar 

  13. Tarski, A., Givant, S.R.: A formalization of set theory without variables, vol. 41. American Mathematical Soc. (1987)

    Google Scholar 

  14. Winter, M.: Products in categories of relations. The Journal of Logic and Algebraic Programming 76(1), 145–159 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zieliński, B., Maślanka, P.: Weak n-ary relational products in allegories. Axioms 3(4), 342–357 (2014)

    Article  MATH  Google Scholar 

  16. Zieliński, B., Maślanka, P., Sobieski, Ś.: Allegories for database modeling. In: Cuzzocrea, A., Maabout, S. (eds.) MEDI 2013. LNCS, vol. 8216, pp. 278–289. Springer, Heidelberg (2013), http://dx.doi.org/10.1007/978-3-642-41366-7_24

    Chapter  Google Scholar 

  17. Zieliński, B., Maślanka, P., Sobieski, Ś.: Modalities for an allegorical conceptual data model. Axioms 3(2), 260–279 (2014), http://www.mdpi.com/2075-1680/3/2/260

    Article  MATH  Google Scholar 

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Correspondence to Bartosz Zieliński .

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Zieliński, B. (2015). Generalised N-ary Relations and Allegories. In: Kahl, W., Winter, M., Oliveira, J. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2015. Lecture Notes in Computer Science(), vol 9348. Springer, Cham. https://doi.org/10.1007/978-3-319-24704-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-24704-5_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24703-8

  • Online ISBN: 978-3-319-24704-5

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