Abstract
This paper is concerned with the formalization of data bases in terms of first order logic concepts. Two approaches to such a formalization are first considered. In the first approach the elementary facts as well as the general statements are considered as the proper axioms of a first order theory, whereas in the second one the elementary facts are considered as defining an interpretation of a first order theory whose proper axioms are the sole general statements. These two approaches are discussed and contrasted with regard to the representation of negative information, querying and integrity checking. Both of them impose a uniform use of general statements; so, a third approach, which is an extension of the second one, is proposed. It enables one to use some general statements as derivation rules while others are used as integrity rules. Finally, due to their importance in relational data bases, some results specific to functional and multivalued dependency statements are stated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Beeri, C., Fagin, R., and Howard, H.J. [1977] A Complete Axiomatization for Functional and Multivalued Dependencies in Data Base Relations, Proceedings of ACM SIGMOD Conference, Toronto, Canada, August 1977, 47–61.
Chang, C. L. and Lee, R.C.T. [1973] Symbolic Logic and Mechanical Theorem Proving, Computer Science and Applied Mathematics, Series of Academic Press, Inc., New York, N.Y., 1973.
Chang, C. L. [1976] Deduce: A Deductive Language for Relational Data Bases, In Pattern Recognition and Artificial Intelligence (C. H. Chen, Ed.), Academic Press, New York, N.Y., 1976, 108–134.
Codd, E. F. [1974] Recent Investigation in Relational Data Base Systems, Proceedings of IFIP Congress 74, Stockholm, Sweden, August 1974, 1017–1921.
Colmerauer, A. [1975] Les grammaires de métamorphose, T.R. Groupe d’ Intelligence Artificielle, Marseille, France, Nov. 1975.
Date, C. J. [1977] An Introduction to Database Systems (Second Edition), Addison-Wesley Publishing Company, Reading, Massachusetts, 1977.
Demolombe, R. and Nicolas, J. M. [1976] Knowledge Representation and Evolutivity in Data Base Management Systems, T. Report CERT — LDB — 76/5, Toulouse, France, Nov. 1976.
Fishman, D. H. and Minker, J. [1975] Π-Representat ion. A Clause Representation for Parallel Search, Artificial Intelligence 6, 2 (1975), 103–127.
Florentin, J. J. [1974] Consistency Auditing of Data Bases, The Computer Journal 17,1 (Feb. 1974), 52–58.
Kellogg, C., Klahr, P., and Travis, L. [1976] A Deductive Capability for Data Base Management, Proceedings of 2nd Int. Conference on VLDB, Brussels, Belgium, Sept. 1976, 181–196.
Kleene, S. C. [1968] Mathematical Logic, John Wiley and Sons, Inc., New York, 1968.
Kowalski, R. A. [1976] Logic and Data Bases, Logic Programming Meeting, Imperial College, London, May 1976.
McSkimin, J.R. and Minker, J. [1978] A Predicate Calculus Based Semantic Network for Question-Answering Systems, In Associative Networks — The Representation and Use of Knowledge in Computers (N. Findler, Ed.), Adacemic Press, New York, N.Y., 1978 (in press).
McSkimin, J. R. and Minker, J. [1977] The Use of a Semantic Network in a Deductive Question-Answering System, Proceedings IJCAI-77, Cambridge, Massachusetts, 1977, 50–58.
Mendelson, E. [1964] Introduction to Mathematical Logic, D. Van Nostrand, New York, 1964.
Nicolas, J.M. and Syre, J.C. [1974] Natural Question Answering and Automatic Deduction in the System Syntex, Proceedings of IFIP Congress 1974, Stockholm, Sweden, August 1974, 595–599.
Nicolas, J.M., Demolombe, R. and Yazdanian, K. [1976] Contribution of Predicate Logic to Data Bases, T. Report CERT — LBD 76/1, Toulouse, France, Sept. 1976.
Nicolas, J. M. and Demolombe, R. [1977] A short note on the use of first order logic in the formalization of functional and multivalued dependencies, T. Report CERT — LBD 77/1, Toulouse, France, Sept. 1977.
Nicolas, J.M. and Yazdanian, K. [1978] Integrity Checking in Deductive Data Bases, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, N.Y., 1978, 325–344.
Reiter, R. [1977] An Approach to Deductive Question-Answering, BBN Report No. 3649, Cambridge, Mass., Sept. 1977.
Roussel, P [1975] PROLOG — Manuel de référence et dutilisation, Groupe d’Intelligence Artificielle, Marseille, France Sept, 1975.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Plenum Press, New York
About this chapter
Cite this chapter
Nicolas, J.M., Gallaire, H. (1978). Data Base: Theory vs. Interpretation. In: Gallaire, H., Minker, J. (eds) Logic and Data Bases. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3384-5_2
Download citation
DOI: https://doi.org/10.1007/978-1-4684-3384-5_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-3386-9
Online ISBN: 978-1-4684-3384-5
eBook Packages: Springer Book Archive