Abstract
We present a generalization of the relational model of data in which disjunctive and negative information can be represented explicitly and manipulated. There are situations where the closed world assumption to infer negative facts is not valid or undesirable and there is a need to represent and reason with negation explicitly. We consider explicit negation in the context of disjunctive databases as there is an interesting interplay between these two types of information. Disjunctive paraconsistent relations are introduced as the main structure in this model. The relational algebra is appropriately generalized to work on disjunctive paraconsistent relations and their correctness is established.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R. Bagai and R. Sunderraman. A paraconsistent relational data model. International Journal of Computer Mathematics, 55(3), 1995.
E.F. Codd. A relational model for large shared data banks. Communications of the ACM, 13(6):377–387, June 1970.
E.F. Codd. Missing information (applicable and inapplicable) in relational databases. SIGMOD Record, 15(4):53–78, December 1986.
E. Gelenbe and G. Hebrail. A probability model of uncertainity in databases. In Proceedings of the International Conference on Data Engineering. IEEE Computer Society Press, 1986.
J. Grant. Null values in a relational database. Information Processing Letters, 6(5):156–157, October 1977.
J. Grant. Incomplete information in a relational database. Fundamental Informaticae, III(3):363–378, 1980.
J. Grant and J. Minker. Answering queries in indefinite databases and the null value problem. In P. Kanellakis, editor, Advances in Comput ng Research, pages 247–267. JAI Press, Greenwich, CT, 1986.
T. Imieliński and W. Lipski. Incomplete information in relational databases. Journal of the ACM, 31(4):761–791, October 1984.
K.-C. Liu and R. Sunderraman. Indefinite and maybe information in relational databases. ACM Transactions on Database Systems, 15(1):1–39, 1990.
K.-C. Liu and R. Sunderraman. A generalized relational model for indefinite and maybe information. IEEE Transactions on Knowledge and Data Engineering, 3(1):65–77, 1991.
D. Maier. The Theory of Relational Databases. Computer Science Press, Rockville, Maryland, 1983.
J. Minker and C. Ruiz. On extended disjunctive logic programs. In J. Komorowski and Z.W. Ras, editors, Proceedings of the Seventh International Symposium on Methodologies for Intelligent Systems, pages 1–18. Lecture Notes in AI, Springer-Verlag, New York, June 1993.
K.V.S.V.N. Raju and A.K. Majumdar. Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems. ACM Transactions on Database Systems, 13(2):129–166, 1988.
R. Reiter. Towards a logical reconstruction of relational database theory. In M. Brodie, J. Mylopoulos, and J.W. Schmidt, editors, On Conceptual Modeling, pages 191–238. Springer-Verlag, Berlin and New York, 1984.
Raymond Reiter. On closed world data bases. In Hervé Gallaire and Jack Minker, editors, Logic and Data Bases, pages 55–76. Plenum Press, 1978.
R. Sunderraman. Deductive databases with conditional facts. Lecture Notes in Computer Science, 696:162–175, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sunderraman, R. (1997). Modeling negative and disjunctive information in relational databases. In: Hameurlain, A., Tjoa, A.M. (eds) Database and Expert Systems Applications. DEXA 1997. Lecture Notes in Computer Science, vol 1308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022043
Download citation
DOI: https://doi.org/10.1007/BFb0022043
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63478-2
Online ISBN: 978-3-540-69580-6
eBook Packages: Springer Book Archive