Deductive object oriented schemas

  • Dimitri Theodoratos
Session 1: Advanced Schema Design
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1157)


Current Object Oriented (OO) Database schema structures allow isa relationships and multiple inheritance. We extend these structures with features from semantic modelling that are not traditionally supported by OO schemas: disjointness of classes and class intersection inclusion into other classes as well as negations of these statements. Formally we represent schemas as sets of first order monadic formulas. We provide a formal system for schemas that is sound and complete both for finite and unrestricted implications. Based on it and on well known algorithms we show that checking formula deduction is polynomial. Consistency is characterized completely in two alternative ways in terms of formula deduction. We show that these results allow us to deal efficiently with the issues of incremental/intelligent consistency checking, redundancy removal, minimal representation and updating in OO schemas.


Object class structures First order theory Axiomatization Deduction Consistency 


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  1. [1]
    S. Abiteboul and R. Hull. IFO: A formal semantic database model. ACM Trans. Database Systems, 12(3):525–565, 1987.Google Scholar
  2. [2]
    S. Abiteboul and P. C. Kanellakis. The two facets of object-oriented data models. Data & Knowledge Engineering, 14(2):3–7, 1991.Google Scholar
  3. [3]
    H. Arisawa and T. Miura. On the properties of extended inclusion dependencies. In Proc. of Intl. Conf. on Very Large Data Bases, pages 449–456, 1986.Google Scholar
  4. [4]
    W. W. Armstrong. Dependency structures of database relationships. In Proc. IFIP 74, North Holland, Amsterdam, pages 580–583, 1974.Google Scholar
  5. [5]
    M. Atkinson, D. DeWitt, D. Maier, F. Bancilhon, K. Dittrich, and S. Zdonik. The object-oriented database system manifesto. In Proc. of 1st Intl. Conf. on Deductive and Object Oriented Databases, pages 40–57, 1989.Google Scholar
  6. [6]
    P. Atzeni and D. S. Parker. Formal properties of net-based knowledge represenation schemes. Data & Knowledge Engineering, 3:137–147, 1988.Google Scholar
  7. [7]
    P. Atzeni and D. S. Parker. Set containment inference and syllogisms. Theoretical Computer Science, 62:39–65, 1988.Google Scholar
  8. [8]
    P. Atzeni and D. S. Parker. Algorithms for set containment inference. In F. Bancilhon and P. Buneman, editors, Advances in Database Programming Languages, pages 43–65. ACM Press, Frontier Series, 1990.Google Scholar
  9. [9]
    G. Ausiello, A. D'Atri, and D. Saccà. Graph algorithms for functional dependency manipulation. Jour. of the ACM, 30(4):752–766, Oct. 1983.Google Scholar
  10. [10]
    G. D. Battista and M. Lenzerini. Deductive entity relationship modeling. IEEE Transactions on Knowledge and Data Engineering, 5(3):439–450, 1993.Google Scholar
  11. [11]
    C. Beeri and P. Berstein. Computational problems related to the design of normal form relational schemas. ACM Trans. Database Syst, 4(1):30–59, Mar 1979.Google Scholar
  12. [12]
    D. Calvanese and M. Lenzerini. Making object-oriented schemas more expressive. In Proc. of the Intl. Conf. on Principles of Database Systems, pages 243–254, 1994.Google Scholar
  13. [13]
    C.-L. Chang and R. C.-T. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.Google Scholar
  14. [14]
    S. B. Dreben and D. W. Goldfarb. The Decision Problem: Solvable Classes of Quantificational formulas. Addison-Wesley, Reading, MA, 1979.Google Scholar
  15. [15]
    R. Fagin, G. M. Kuper, J. Ullman, and M. Vardi. Updating logical databases. In P. Kanellakis and F. Preparata, editors, Advances in computing Research, volume 3, pages 1–18. JAI Press, Greenwhich, CT, 1986.Google Scholar
  16. [16]
    R. Fagin, J. Ullman, and M. Vardi. On the semantics of updates in databases. In Proc. Second ACM Symp. on Principles of Database Systems, Atlanta, GA, pages 352–365, 1983.Google Scholar
  17. [17]
    R. Hull and R. King. Semantic Database Modeling: Survey, Applications and Research issues. ACM Computing Surveys, 19(3):201–260, 1987.Google Scholar
  18. [18]
    P. Kanellakis, C. Lécluse, and P. Richard. Introduction to the data model. In F. Bancilhon, C. Delobel, and P. Kanellakis, editors, Building an Object Oriented Database system, the story of O2. Morgan Kaufmann Publishers, 1992.Google Scholar
  19. [19]
    H. A. Kautz, M. J. Kearns, and B. Selman. Horn approximations of empirical data. Artificial Intelligence, 74(1), mar 1995.Google Scholar
  20. [20]
    M. Lenzerini. Class hierachies and their complexity. In F. Bancilhon and P. Buneman, editors, Advances in Database Programming Languages, pages 43–65. ACM Press, Frontier Series, 1990.Google Scholar
  21. [21]
    B. Nebel. Belief revision and default reasoning: syntax based approaches. In Proc. of the Second Intl. Conf. on Principles of Knowledge Representation and Reasoning, pages 417–428, 1991.Google Scholar
  22. [22]
    D. Theodoratos. Monadic databases with equality. In Proc. of the Intl. Symp. on Mathematical Fundamentals of Database and Knowledge Base Systems, pages 74–88. Springer-Verlag, LNCS 495, 1991.Google Scholar
  23. [23]
    J. D. Ullman. Principles of Database and Knowledge-Base Systems, volume 2. Computer Science Press, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Dimitri Theodoratos
    • 1
  1. 1.University of IoanninaGreece

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