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Deductive database theories*

Published online by Cambridge University Press:  07 July 2009

John Grant  and
Jack Minker
John Grant
Affiliation:
Department of Computer and Information Sciences, Towson State University, Towson, Maryland 21204, USA
Jack Minker
Affiliation:
Department of Computer Science and University of Maryland Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742, USA
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Abstract

This paper surveys a variety of deductive database theories. Such theories differ from one another in the set of axioms and metarules that they allow and use. The following theories are discussed: relational, Horn, and stratified in the text; protected, disjunctive, typed, extended Horn, and normal in the appendix. Connections with programming in terms of the declarative, fixpoint, and procedural semantics are explained. Negation is treated in several different ways: closed world, completed database, and negation as failure. For each theory examples are given and implementation issues are considered.

Type
Research Article
Information
The Knowledge Engineering Review , Volume 4 , Issue 4 , December 1989 , pp. 267 - 304
Copyright
Copyright © Cambridge University Press 1989

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References

Gallaire, H and Minker, J, Eds, 1978. Logic and Databases, New York: Plenum.Google Scholar
Gallaire, H, Minker, J and Nicolas, J, 1984. “Logic and databases: A deductive approach” ACM Computing Surveys 16 153–185.CrossRefGoogle Scholar
Minker, J, 1987. “Deductive databases: An overview of some alternative theories” In Ras, ZW and Zemankova, M, Eds, Methodologies for Intelligent Systems, Amsterdam: Elsevier, pp. 148–158.Google Scholar
Minker, J, Ed., 1988. Foundations of Deductive Databases and Logic Programming, California: Morgan Kaufmann.Google Scholar
Minker, J, 1988a. “Perspectives in deductive databases” The Journal of Logic Programming 5 33–60.CrossRefGoogle Scholar
Ullman, JD, 1988. Principles of Database and Knowledge-Base Systems, Volumes I and II, Maryland: Computer Science Press.Google Scholar
Chang, CL and Lee, RTC, 1973. Symbolic Logic and Mechanical Theorem Proving, New York: Academic Press.Google Scholar
Enderton, HB, 1972. A Mathematical Introduction to Logic, New York: Academic Press.Google Scholar
Lloyd, JW, 1987. Foundations of Logic Programming, Second Extended Edition, New York: Springer-Verlag.CrossRefGoogle Scholar
Loveland, D, 1978. Automated Theorem Proving: A Logical Basis, Amsterdam: Elsevier North-Holland.Google Scholar
Mendelson, E, 1978. Introduction to Mathematical Logic, 2nd Ed., New York: van Nostrand-Reinhold.Google Scholar
Grant, J and Minker, J, 1990. “Integrity constraints in knowledge based Systems”, In Adeli, H, Ed., Knowledge Engineering, Vol. II, Applications, New York: McGraw-Hill, pp. 1–25.Google Scholar
Nicolas, J and Gallaire, H, 1978. “Data base: Theory vs interpretation” In Gallaire, H and Minker, J, Eds, Logic and Databases, New York: Plenum, pp. 33–54.Google Scholar
van Emden, MH and Kowalski, R, 1976. “The semantics of predicate logic as a programming language” Journal of the ACM 23 733–742.CrossRefGoogle Scholar
Chan, C, 1988. “Constructive negation based on the completed database”, In Kowalski, RA and Bowen, KA, Eds, Logic Programming Proceedings of the Fifth International Conference and Symposium,Massachusetts:The MIT Press, pp. 111–125.Google Scholar
Clark, KL, 1978. “Negation as failure” In Gallaire, H and Minker, J, Eds, Logic and Databases, New York: Plenum, pp. 293–322.Google Scholar
Reiter, R, 1978. “On closed world databases” In Gallaire, H and Minker, J, Eds, Logic and Databases, New York: Plenum, pp. 149–178.Google Scholar
Shepherdson, JC, 1988. “Negation in logic programming” In Minker, J, Ed., Foundations of Deductive Databases and Logic Programming, California: Morgan Kaufmann, pp. 19–88.CrossRefGoogle Scholar
Apt, KR, Blair, HA and Walker, A, 1988. “Towards a theory of declarative knowledge” In Minker, J, Ed., Foundations of Deductive Databases and Logic Programming, California: Morgan Kaufmann, pp. 89–148.CrossRefGoogle Scholar
Chandra, A and Harel, D, 1985. “Horn clause queries and generalizations” The Journal of Logic Programming 2 1–15.CrossRefGoogle Scholar
Gelfond, M, Przymusinska, H and Przymusinski, T, 1989. “On the relationship between circumscription and negation as failure” Artificial Intelligence 38 75–94.CrossRefGoogle Scholar
Naqvi, SA, 1986. “A logic for negation in database Systems” In Minker, J, Ed., Proceedings of the Workshop on Foundations of Deductive Databases and Logic Programming Washington, D.C., pp. 378–387.Google Scholar
Naqvi, SA and Tsur, S, 1989. A Logical Language for Data and Knowledge Bases, Maryland: Computer Science Press.Google Scholar
Przymusinski, TC, 1988a. “On the declarative semantics of deductive databases and logic programs”, In Minker, J, Ed., Foundations of Deductive Databases and Logic Programming, California: Morgan Kaufmann, pp. 193–216.CrossRefGoogle Scholar
Przymusinski, TC, 1988b. “On the declarative and procedural semantics of logic programs” Journal of Automated Reasoning 4.Google Scholar
Van Gelder, A, 1988. “Negation as failure using tight derivations for general logic programs” In Minker, J, Ed., Foundations of Deductive Databases and Logic Programming, New York: Morgan Kaufmann, pp. 149–176.CrossRefGoogle Scholar
Minker, J and Perlis, D, 1985. “Computing protected circumscription” The Journal of Logic Programming 4 pp. 235–249.CrossRefGoogle Scholar
Bossu, G and Siegel, P, 1985. “Saturation, non-monotonic reasoning and the closed-world assumption” Artificial Intelligence 25 13–63.CrossRefGoogle Scholar
Grant, J and Minker, J, 1986. “Answering queries in indefinite databases and the null value problem” In Kanellakis, P, Ed., Advances in Computing Theory, Vol. 3, The Theory of of Databases, JAI Press, pp. 247–267.Google Scholar
Henschen, LJ and Park, H-S, 1988. “Compiling the GCWA in indefinite deductive databases”, In Minker, J, Ed., Foundations of Deductive Databases and Logic Programming, California: Morgan Kaufmann, pp. 295–438.Google Scholar
Lobo, J, Minker, J and Rajasekar, A, 1988. “Weak completion theory for non-Horn programs”, In Kowalski, RA and Bowen, KA, Eds, Logic Programming Proceedings of the Fifth International Conference and Symposium, Massachusetts: MIT Press, pp. 828–842.Google Scholar
Minker, J, 1982. “On indefinite databases and the closed world assumption”, In Proc. of the 6th Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science No. 138,New York:Springer-Verlag, pp. 292–308.CrossRefGoogle Scholar
Minker, J and Rajasekar, A, 1989. “A fixpoint semantics for non-Horn logic programs” The Journal of Logic Programming.CrossRefGoogle Scholar
Minker, J and Zanon, G, 1982. “An extension to linear resolution with selection function” Information Processing Letters 14 pp. 191–194.CrossRefGoogle Scholar
Rajasekar, A, Lobo, J and Minker, J, 1989. “Weak generalized closed world assumption”, Journal of Automated Reasoning 5 293–307.CrossRefGoogle Scholar
Ross, KA and Topor, RW, 1988. “Inferring negative information from disjunctive databases” Journal of Automated Reasoning 4 397–424.CrossRefGoogle Scholar
Yahya, A and Henschen, LJ, 1985. “Deduction in non-Horn databases” Journal of Automated Reasoning 1 141–160.CrossRefGoogle Scholar
Reiter, R, 1984. “Towards a logical reconstruction of relational database theory”, In Brodie, ML, Mylopoulos, J and Schmidt, JW, Eds, On Conceptual Modelling, New York: Springer-Verlag, pp. 191–233.CrossRefGoogle Scholar
Lloyd, JW and Topor, RW, 1984. “Making Prolog more expressive” Journal of Logic Programming 1 225–240.CrossRefGoogle Scholar
Lloyd, JW and Topor, RW, 1985. “A basis for deductive database Systems” Journal of Logic Programming 2 93–109.CrossRefGoogle Scholar
Lloyd, JW and Topor, RW, 1986. “A basis for deductive database Systems II” Journal of Logic Programming 3 pp. 55–67.CrossRefGoogle Scholar
Przymusinski, TC, 1989. “Every logic program has a natural stratification and an iterated least fixed point model” In Proc. of ACM PODS 11–21.CrossRefGoogle Scholar
Van Gelder, A, Ross, KA and Schlipf, JS, 1988. “Unfounded sets and well-founded semantics for general logic programs” In Proc. of ACM PODS 221–230.CrossRefGoogle Scholar