Abstract
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.
Research carried out as part of the ERCIM Fellowship Program and financed by the Commission of the European Communities while the author was visitor at the INRIA, Rocquencourt.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
S. Abiteboul and R. Hull. IFO: A formal semantic database model. ACM Trans. Database Systems, 12(3):525–565, 1987.
S. Abiteboul and P. C. Kanellakis. The two facets of object-oriented data models. Data & Knowledge Engineering, 14(2):3–7, 1991.
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.
W. W. Armstrong. Dependency structures of database relationships. In Proc. IFIP 74, North Holland, Amsterdam, pages 580–583, 1974.
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.
P. Atzeni and D. S. Parker. Formal properties of net-based knowledge represenation schemes. Data & Knowledge Engineering, 3:137–147, 1988.
P. Atzeni and D. S. Parker. Set containment inference and syllogisms. Theoretical Computer Science, 62:39–65, 1988.
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.
G. Ausiello, A. D'Atri, and D. Saccà. Graph algorithms for functional dependency manipulation. Jour. of the ACM, 30(4):752–766, Oct. 1983.
G. D. Battista and M. Lenzerini. Deductive entity relationship modeling. IEEE Transactions on Knowledge and Data Engineering, 5(3):439–450, 1993.
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.
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.
C.-L. Chang and R. C.-T. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.
S. B. Dreben and D. W. Goldfarb. The Decision Problem: Solvable Classes of Quantificational formulas. Addison-Wesley, Reading, MA, 1979.
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.
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.
R. Hull and R. King. Semantic Database Modeling: Survey, Applications and Research issues. ACM Computing Surveys, 19(3):201–260, 1987.
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.
H. A. Kautz, M. J. Kearns, and B. Selman. Horn approximations of empirical data. Artificial Intelligence, 74(1), mar 1995.
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.
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.
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.
J. D. Ullman. Principles of Database and Knowledge-Base Systems, volume 2. Computer Science Press, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Theodoratos, D. (1996). Deductive object oriented schemas. In: Thalheim, B. (eds) Conceptual Modeling — ER '96. ER 1996. Lecture Notes in Computer Science, vol 1157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019915
Download citation
DOI: https://doi.org/10.1007/BFb0019915
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61784-6
Online ISBN: 978-3-540-70685-4
eBook Packages: Springer Book Archive