Abstract
In this paper, we consider logical consequences for reasoning about functional, multivalued, and join dependencies in partial knowledge bases. The standard consequence, strong consequence, and the weak consequence are characterized. We prove that reasoning based on the standard logical consequence is equivalent to reasoning based on the strong logical consequence. In addition, we prove that reasoning based on the standard logical consequence and reasoning based on the weak logical consequence are not equivalent. We also define a formal system FSED for reasoning about existence dependencies. We prove that the formal system FSED is sound and complete. We state the connection between existence and functional dependencies: reasoning about existence dependencies based on the corresponding logical consequence and reasoning about functional dependencies based on the standard logical consequence are equivalent.
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References
Abiteboul, S., Hull, R., Vianu, V.: Foundation of Databases. Addison-Wesley, Reading (1995)
Cood, E.F.: The Relational Model for Database Management. Addison-Wesley, Reading (1990)
Date, C.J.: Database in Depth: Relational Theory for Practitioners. O’Reilly, Sebastopol (2005)
Date, C.J.: Why Three- and Four-Valued Logic Don’t Work, pp. 2000–2006. Apress (2006)
Date, C.J.: Logic and Databases: The Roots of Relational Theory. Trafford Publishing (2007)
Maleković, M.: A Combined Algorithm for Testing Implications of Functional and Multivalued Dependencies. Informatica, An International Journal of Computing and Informatics 17, 277–283 (1993)
Maleković, M.: A Sound and Complete Axiomatization of Functional Dependencies: A Formal System with Only Two Inference Rules. Informatica, An International Journal of Computing and Informatics 19, 407–408 (1995)
Maleković, M.: Reasoning about Dependencies in Partial Knowledge Bases. In: Proceedings of 9th IEEE International Conference on Intelligent Engineering Systems, INES 2005, pp. 135–139 (2005)
Pascal, F.: Practical Issues in Database Management. Addison-Wesley, Reading (2000)
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© 2009 Springer-Verlag Berlin Heidelberg
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Maleković, M., Čubrilo, M., Rabuzin, K. (2009). Logical Consequences in Partial Knowledge Bases. In: Rudas, I.J., Fodor, J., Kacprzyk, J. (eds) Towards Intelligent Engineering and Information Technology. Studies in Computational Intelligence, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03737-5_27
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DOI: https://doi.org/10.1007/978-3-642-03737-5_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03736-8
Online ISBN: 978-3-642-03737-5
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