Abstract
A meta-logic statement over a language is characterised by a formula in typed ω-order λ-calculus. The head of the λ-term corresponding to a meta-logic statement is always a constant when it is in normal form. It is shown that both deductive database statements and integrity constraints, particularly those involving aggregate operations, can be represented conveniently in meta-logic statements. A special case of Huet’s unification algorithm is considered on the domain of meta-logic terms and a proof procedure based on this unification is presented to answer database queries and to verify integrity constraints. Although, the main focus is to handle deductive databases problems, the results of this paper deal indirectly with a metalevel extension of first-order logic programming.
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References
H.Gallaire, J.Minker, and J.-M.Nicolas, “Logic and databases - a deductive approach,” ACM Computing Surveys,Vol. 16, No.2, pp. 153–185, (1984).
H.Gallaire, “Logic databases vs deductive databases,” Proceedings of Logic Programming Workshop, pp. 608–622, Algarve, Portugal, (1983).
A.Thayse (ed.), From Modal Logic to Deductive Databases,John Wiley & Sons, (1989).
Y.Y.Leung and D.L.Lee, “Logic approaches for deductive databases,” IEEE Expert, (Winter 1988 ).
J.W.Lloyd, “An introduction to deductive database systems,” The Australian Computer Journal, Vol. 15, No. 2, pp. 52–57, (May 1983).
J.Minker, “Perspectives in deductive databases,” Journal of Logic Programming, Vol. 5, pp. 33–60, (1988).
C.J.Date, An Introduction to Database Systems, Volt, Addison Wesley, (1985).
E.B.Fentandez, R.C.Summers, and C.Wood, Database Security and Integrity, Addison Wesley, (1981).
J.D.Ullman, Principles of Database Systems, 2nd edition, Computer Science Press International, Inc, Maryland, USA, (1984).
R.A.Kowalski, “Logic programming with integrity constraints,” Workshop on Logic Programming, Imperial College, London, (1989).
S.K.Das and M.H.Williams, “Integrity checking methods in deductive databases: A comparative evaluation,” Proceedings of the 7th British National Conference on Databases, pp. 85–116, Cambridge University Press, (1989).
J.W.Lloyd and R.W.Topor, “A basis for deductive database systems,” Journal of Logic Programming, Vol. 2, No.2, pp. 93–109, (1985).
H.Decker, “Integrity enforcements on deductive databases,” L.Kerschberg (ed.): Proceedings of the First International Conference on Expert Database Systems, pp. 271–285, Charleston, South Carolina, (April 1986).
F.Sadri and R.A.Kowalski, “An application of general purpose theorem-proving to database integrity,” J.Minker (ed.): Proceedings of the Workshop on Foundations of Deductive Databases and Logic Programming, (1987).
T.-W.Ling, “Integrity constraint checking in deductive databases using the Prolog not-predicate,” Data & Knowledge Engineering, Vol. 2, pp. 145–168, (1987).
P.Asirelli, M.D.Santis, and M.Martelli, “Integrity constraint in logic databases,” Journal of Logic Programming, Vol. 3, pp. 221–232, (1985).
S.K.Das and M.H.Williams, “A path finding method for checking integrity in deductive databases,” Data & Knowledge Engineering, Vol. 4, pp. 223–244, Elsevier Science Publishers B.V. ( North-Holland ), (1989).
S.K.Das and M.H.Williams, “Extending integrity maintenance capability in deductive databases,” Proceedings of the UK ALP-90 Conference, Intellect, Oxford, Bristol, (March 1990).
W.Snyder and J.Gallier, “Higher-order unification revisited: Complete sets of transformations,” Journal of Symbolic Computation, Vol. 8, pp. 101–140, (1989).
H.P.Barendregt, “The lambda calculus: its syntax and semantics,” JBarwise et al.(ed.): Studies in Logic and The Foundations of Mathematics, Vol.103, North-Holland, (1984).
S.K.Das, Integrity constraints in deductive databases, Department of Computer Science, Heriot-Watt University, PhD Thesis, (1990).
P.M.Hill and J.W.Lloyd, “Analysis of meta-programs,” HAbramson and M.H.Rogers (eds.): Meta programming in Logic Programming, pp. 23–51, MIT Press, (1989).
V.S.Subrahmanian, “A simple formulation of the theory of metalogic programming,” HAbramson and M.H.Rogers (eds.): Meta-programming in Logic Programming, pp. 65–101, MIT Press, (1989).
J.-M.Nicolas, “Logic for improving integrity checking in relational databases,” Acta Informatica, Vol. 18, pp. 227–253, (1982).
G.P.Huet, “A unification algorithm for typed lambda-calculus,” Theoretical Computer Science, Vol. 1, pp. 27–57, (1975).
P.B.Andrews, An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, Academic Press, Inc., (1986).
A.Church, “A formulation of the simple theory of types,” Journal of Symbolic Logic, Vol. 5, pp. 56–68, (1940).
J.W.Lloyd and R.W.Topor, “Making Prolog more expressive,” Journal of Logic Programming, Vol. 1, No.3, pp. 225–240, (1984).
K.R.Apt and M.H.Van Emden, “Contributions to the theory of logic programming,” Journal of the Association for Computing Machinery, Vol. 29, pp. 841–862, (July 1982).
D.A.Miller and G.Nadathur, “Higher-order logic programming,” E.Shapiro (ed.): Proceedings of the 3rd International Conference on Logic Programming, pp. 448462, Springer-Verlag, London, U.K, (July 1986).
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Das, S.K. (1992). Specifying Deductive Databases and Integrity Constraints in Meta-logic. In: Harper, D.J., Norrie, M.C. (eds) Specifications of Database Systems. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3864-8_4
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DOI: https://doi.org/10.1007/978-1-4471-3864-8_4
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