Abstract
We describe a new approach for improving the evaluation of queries with quantifiers. We first introduce the concept of constructive evaluation as a formalization of a principle common to the methods that have been proposed for answering quantified queries. Relying on this concept, we define the class of constructively domain independent (cdi) formulas. We show that cdi queries can be constructively evaluated by searching only the relations they refer to. Therefore, cdi queries admit domain independent evaluations as soon as they do not explicitly refer to the database domain. Then, we define rewritings that translate general quantified queries into expressions amenable to efficient constructive evaluations. These rewritings preserve logical equivalence, hence do not compromise the semantics of queries. They are based on the generation from a query of the ranges and co-ranges of its variables. We show that the rewritings we propose permit to optimize the evaluation of cdi queries. They also reduce queries from several solvable subclasses of domain independent formulas to cdi queries, hence permitting their domain independent evaluation.
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9. References
Bry, F., Decker, H. and Manthey, R. A Uniform Approach to Constraint Satisfaction and Constraint Satisfiability in Deductive Databases. In Proc. EDBT '88. March, 1988.
Bocca, J. On the Evaluation Strategy of EDUCE. In Proc. ACM Int. Conf. on the Management of Data (SIGMOD '86). Washington, D.C., May, 1986.
Bocca, J. and Bailey, P. On Prolog-DBMS connections: A Step forward from EDUCE. In Proc. Alvey Symp. on PROLOG and Databases. Coventry, UK, 1987.
Bry, F. Towards an Efficient Evaluation of General Queries: Quantifier and Disjunction Processing Revisisited. In Proc. ACM Int. Conf. on Management of Data (SIGMOD '89). Portland, Oregon, May 31-June 2, 1989. ECRC Report TR-KB-27, Apr. 1988.
Bry, F. Logic Programming as Constructivism: A Formalization and its Application to Databases. In Proc. 8th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Databases Systems (PODS '89). Philadelphia, Pennsylvania, March 29–31, 1989. ECRC Report IR-KB-54, Sept. 1988.
Ceri, S. and Gottlob, G. Translating SQL in Relational Algebra: Optimization, Semantics and Equivalence of SQL Queries. IEEE Trans. SE-11(4), April, 1985.
Cholvy, L. Interrogation d'une Base de Règle. Technical Report 2/3274/DERI, ONERACERT, Toulouse, France, Feb., 1987. in French.
Codd, E. Database Systems — Courant Computer Science Symp. Prentice Hall, Englewood Cliffs, New Jersey, 1972, Chapter Relational Completeness of Database Sublanguages.
Dayal, U. Processing Queries with Quantifiers: A Horticultural Approach. In Proc. ACM SIGMOD-SIGMACT Symp. Principles of Database SYstems (PODS '83), pages 125–136. Atlanta, March, 1983.
Dayal, U. Of Nests and Trees: A Unified Approach to Processing Queries That Contain Nested Subqueries, Aggregates, and Quantifiers. In Proc. VLDB '87, pages 197–208. August, 1987.
Decker, H. The Range Form of Database Queries, or: How to Avoid Floundering. In Proc. Österreichische Artificial Intelligence Tagung. Igls bei Innbruck, March 28–29, 1989.
Demolombe, R. Syntactical Characterization of a Subset of Domain Independent Formulas. Technical Report, ONERA-CERT, Toulouse, France, 1982.
Di Paola, R.A. The Recursive Unsolvability of the Decision Problem for the Class of Definite Formulas. Jour. of the ACM 16(2), 1969.
Fagin, R. Horn Clauses and Database Dependencies. In 12th Ann. ACM Symp. on Theory of Computing, pages 123–134. 1980.
Huet, G. Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems. Jour. of the ACM 27(4):797–821, October, 1980.
Jarke, M. and Schmidt, J. Query Processing Strategies in the PASCAL/R Relational Database Management System. In Proc. ACM Int. Conf. on Management of Data (SIGMOD '82). June, 1982.
King, J.J. Query Optimization by Semantic Reasoning. Technical Report STAN-CS-81-857, Stanford Univ., Dpt. of Computer Sc., May, 1981.
Kowalski, R.A. Algorithm = Logic + Control. Commun. ACM, Aug., 1979.
Kuhns, J.L. Answering Question by Computer: A Logical Study. Technical Report RM-5428-PR, Rand Corp., 1967.
Lloyd, J.W. and Topor, R.W. A Basis for Deductive Database Systems II. Jour. of Logic Programming 3(1):55–67, 1986.
Manthey, R. and Bry, F. SATCHMO: A Theorem Prover Implemented in Prolog. In Proc. Conf. on Automated Deduction (CADE '88). May, 1988.
Mendelson, E. Introduction to Mathematical Logic. Van Nostrand, New York, 1979.
Nicolas, J.-M. and Demolombe, R. On the Stability of Relational Queries. Technical Report, ONERA-CERT, Jan., 1983.
Nicolas, J.-M. Logic for Improving Integrity Checking in Relational Databases. Acta Informatica 18(3):227–253, Dec., 1981.
Palermo, F. A Data Base Search Problem. In Proc. 4th Symp. on Computer and Information Sc.. 1972.
Schmitt, P. H. A Survey of Rewrite Systems. In Proc. Workshop on Computer Science Logic (CSL '87), pages 235–262. Springer-Verlag (LNCS 329), Oct., 1987.
Troelstra, A.S. Handbook of Mathematical Logic. North-Holland, Amsterdam and New York, 1977, pages 973–1052, Chapter Aspects of Constructive Mathematics.
Van Gelder, A. and Topor, R.W. Safety and Correct Translation of Relational Calculus Formulas. In Proc. 6th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems (PODS '87), pages 313–327. 1987.
Vieille, L. Recursive Axioms in Deductive Databases: The Query-Subquery Approach. In Proc. 1st Int. Conf. on Expert Database Systems. Charleston, South Carolina, 1986.
Vieille, L. From QSQ towards QoSaQ: Global optimization in Recursive Queries. In Proc. 2nd Int. Conf. on Expert Database Systems. Tyson Corner, Virginia, 1988.
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Bry, F. (1989). Logical rewritings for improving the evaluation of quantified queries. In: Demetrovics, J., Thalheim, B. (eds) MFDBS 89. MFDBS 1989. Lecture Notes in Computer Science, vol 364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51251-9_8
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DOI: https://doi.org/10.1007/3-540-51251-9_8
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