A Calculus of Typed Relations

  • Wendy MacCaull
  • Ewa Orłowska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)


A calculus of typed relations subsuming the classical relational database theory is presented. An associated sound and complete deduction mechanism is developed. The formulation is generalized to deal with nondeterministic databases and information relations in the rough set-style.


Relational proof system typed relations relational database nondeterministic databases information relations 


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  1. 1.
    Buszkowski, W., Orłowska, E.: Indiscernibility-based formalization of dependencies in information systems. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 293–315. Physica Verlag, Heidelberg (1997)Google Scholar
  2. 2.
    Chandra, A.K., Harel, D.: Computable Queries for Relational Data Bases. J. of Computer and System Sciences 21, 156–178 (1980)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Codd, E.: A relational model for large shared data banks. Communications of the ACM 16, 377–387 (1970)CrossRefGoogle Scholar
  4. 4.
    Cosmadakis, S.: Database theory and cylindric lattices in: A.K. Chondra, editor,Proceedings of the 28th Annual Symposium on Foundations of Computer Science,IEEE Computer Science Press (1987) 411-420. Google Scholar
  5. 5.
    Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference, Complexity. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2002)MATHGoogle Scholar
  6. 6.
    Düntsch, I., Mikulas, S.: Cylindric structures and dependencies in relational databases. J. of Theoretical Computer Science 269, 451–468 (2001)MATHCrossRefGoogle Scholar
  7. 7.
    Imielinski, T., Lipski, W.: The relational model of data and cylindric algebras. J. of Computer and System Sciences 28, 80–102 (1984)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Lipski, W.: On semantic issues connected with incomplete information databases. ACM Transactions on Database Sytems 4, 262–296 (1979)CrossRefGoogle Scholar
  9. 9.
    MacCaull, W.: Proof theory for generalized dependencies for information relations. Fundamenta Informaticae 42, 1–27 (2000)MATHMathSciNetGoogle Scholar
  10. 10.
    MacCaull, W., Orłowska, E.: A logic of typed relations and its applications to relational database theory (preprint)Google Scholar
  11. 11.
    MacCaull, W., Orłowska, E.: Correspondence results for relational proof systems with application to the Lambek calculus. Studia Logica 71, 389–414 (2002)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Orłowska, E.: Algebraic approach to database constraints. Fundamenta Informaticae 10, 57–66 (1987)MATHMathSciNetGoogle Scholar
  13. 13.
    Orłowska, E.: Relational Formalization of Nonclassical Logics. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, pp. 90–105. Springer, Heidelberg (1996)Google Scholar
  14. 14.
    Orłowska, E.: Introduction: What You Always Wanted to Know About Rough Sets. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 1–20. Physica Verlag, Heidelberg (1997)Google Scholar
  15. 15.
    Pawlak, Z.: Rough Sets. Kluwer, Dordrecht (1991)MATHGoogle Scholar
  16. 16.
    Rasiowa, H., Sikorski, R.: The Mathematics of Metamathematics. Polish Science Publishers, Warsaw (1963)MATHGoogle Scholar
  17. 17.
    Simovici, D.A., Tenney, R.L.: Relational Database Systems. Academic Press, London (1995)Google Scholar
  18. 18.
    Ullman, J.: Database and Knowledge-Base Systems, vol. 1. Computer Science Press (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Wendy MacCaull
    • 1
  • Ewa Orłowska
    • 2
  1. 1.Department of Mathematics, Statistics and Computer ScienceSt. Francis Xavier UniversityAntigonishCANADA
  2. 2.National Institute of TelecommunicationsWarsawPoland

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