Advertisement

Indiscernibility-Based Formalization of Dependencies in Information Systems

  • Wojciech Buszkowski
  • Ewa Orlowska
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 13)

Abstract

Various classes of data constraints in information systems are modelled by means of indiscernibility relations induced by sets of attributes. A relational logic is presented that enables us to express these constraints. A proof system for the logic is given and its completeness is proved with respect to a class of algebras of relations generated by indiscernibility relations. Some other classes of models for the logic are defined that correspond to typical kinds of constraints in information systems. Decidability of the validity problem with respect to these classes of models is discussed and some classes of formulas with the decidable validity problem are given.

Keywords

Binary Relation Word Problem Proof System Database Model Proof Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Armstrong, W. W.: (1974) Dependency structures of database relationships. Proceedings IFIP’74, 580–583Google Scholar
  2. [2]
    Beeri, C. and Vardi, M. Y.: (1984) A proof procedure for data dependencies. Journal of the ACM 31, 718–741MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Buszkowski, W. and Orlowska, E.: (1985) On the logic of database dependencies. Proceedings of the Fourth Hungarian Computer Science Conference, 373–383Google Scholar
  4. [4]
    Buszkowski, W. and Orlowska, E.: (1986) Relational calculus and data dependencies. ICS PAS Report 583, WarsawGoogle Scholar
  5. [5]
    Clifford, A. H. and Preston, G. B.: (1964) The Algebraic Theory of Semigroups. Vol. I, American Mathematical Society, ProvidenceGoogle Scholar
  6. [6]
    Codd, E. F.: (1970) A relational model for large shared data banks. Communications of ACM 13, 377–387MATHCrossRefGoogle Scholar
  7. [7]
    Codd, E. F.: (1972) Further normalization of the data base relational model. In: Rustin, R. (ed) Data Base Systems. Prentice—Hall, Englewood Cliffs, NJ, 33–64Google Scholar
  8. [8]
    Davis, M.: (1958) Computability and Unsolvability. McGraw—Hill, New YorkMATHGoogle Scholar
  9. [9]
    Fagin, R. and Vardi, M. Y.: (1986) The theory of data dependencies: a survey. In: Anshel, M. and Gewirtz, W.: (eds) Mathematics of Information Processing. Symposia in Applied Mathematics, Vol 34, 19–72Google Scholar
  10. [10]
    Kanellakis, P. C.: (1990) Elements of relational database theory. In: Van Leeuwen, J. (ed) Handbook of Theoretical Computer Science. Elsevier Science Publishers, 1075–1156Google Scholar
  11. [11]
    Orlowska, E.: (1987) Algebraic approach to database constraints. Fundamenta Informaticae 10,57— 68. See also: Report 182, Langages et Systemes Informatiques, Toulouse, 1983Google Scholar
  12. [12]
    Orlowska, E.: (1988) Relational interpretation of modal logics. In: Andreka, H., Monk, D. and Nemeti, I. Algebraic Logic. Colloquia Mathematica Societatis Janos Bolyai 54, North Holland, Amsterdam, 443–471Google Scholar
  13. [13]
    Rasiowa, H. and Sikorski, R.: (1963) The Mathematics of Metamathematics. Polish Science Publishers, WarsawMATHGoogle Scholar
  14. [14]
    Sagiv, Y., Delobel, C., Parker, D. S. and Fagin, R.: (1981) An equivalence between relational database dependencies and a fragment of propositional logic. Journal of ACM 28, 435–453MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    Tarski, A.: (1941) On the calculus of relations. Journal of Symbolic Logic 6, 73–89MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    Ullman, J.: (1988) Principles of Database and Knowledge Base Systems. Vol. I. Computer Science Press, RockvilleGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Wojciech Buszkowski
    • 1
  • Ewa Orlowska
    • 2
  1. 1.Institute of MathematicsAdam Mickiewicz UniversityPoznanPoland
  2. 2.Institute of TelecommunicationsWarsawPoland

Personalised recommendations