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A Relational Calculus with Set Operators, Its Safety, and Equivalent Graphical Languages
September 1989 (vol. 15 no. 9)
pp. 1038-1052

The authors propose a relational calculus (RC/S) which uses set comparison and set manipulation operators to replace universal quantifiers and negations. It is argued that compared to the Codd relational calculus (RC), RC/S queries are easier to construct and comprehend. It is proved that the expressive power of RC is equivalent to the expressive power of RC/S, and algorithms for translating an RC query into an RC/S query and vice versa are given. A safe RC/S query is defined as one that has finite output and can be evaluated in finite time. Then a subset of RC/S queries, called RC/S* is defined, and it is proved that RC/S* is safe. RC/S* is compared to the existing largest safe subsets of RC, i.e. the evaluable formulas and the allowed formulas. Algorithms are given to transform any evaluable formula into an RC/S* query, and some RC/S* formulas that are not evaluable are given. RC/S* queries can be directly implemented using a graphical language similar to Query-by-Example (QBE). Two different graphical languages are described that are equivalent to the RC/S* in expressive power, and these languages are compared to QBE.

[1] W. A. Abdul-Qader and G. Ozsoyoglu, "A human factors study of two screen oriented query languages: STBE and QBE," Case Western Reserve Univ., Tech. Rep., 1987.
[2] E. F. Codd, "Relational completeness of database sublanguages," inData Base Systems (Courant Computer Science Symp. 6), R. Rustin, Ed. Englewood Cliffs, NJ: Prentice-Hall, 1971.
[3] E. F. Codd, "A database sub-language founded on the relational calculus," inProc. ACM SIGFIDET Workshop Data Description, Access and Control, Nov. 1971, pp. 35-61.
[4] E. F. Codd, "Normalized database structure: A brief tutorial," inProc. ACM SIGFIDET Workshop Data Description, Access and Control, Nov. 1971, pp. 1-7.
[5] H. Decker, "Integrity enforcement in deductive databases," inProc. 1st Int. Conf. Expert Database Systems, pp. 271-285.
[6] R. Demolombe, "Syntactical characterization of a subset of domain independent formulas," ONERACERT, Tech. Rep., 1982.
[7] R. Demolombe, "Assigning meaning to ill-defined queries expressed in predicate calculus language," inAdvances in Data Base Theory, vol. 1, J. Minker and J.-M. Nicolas, Eds. New York: Plenum, 1981.
[8] R. A. DiPaola, "The recursive unsolvability of the decision problem for the class of definite formulas,"J. ACM, vol. 16, no. 2, pp. 324- 324, 1969.
[9] R. Fagin, "Horn clauses and database dependencies,"J. ACM, vol. 29, no. 3, pp. 952-985, Oct. 1982.
[10] A. Gelder, private communication, Jan. 1987.
[11] A. Van Gelder and R. W. Topor, "Safety and correct translation of relational calculus formulas," inProc. ACM Symp. on Principles of Database Syst., 1987, pp. 313-326.
[12] A. Klug, "Abe--A query language for constructing aggregates-byexample," inProc. First Int. Workshop Statistical Database Management, 1981.
[13] A. Klug, "Equivalence of Relational Algebra and Relational Calculus Query Languages Having Aggregate Functions,"J. ACM, Vol. 29, No. 3, July 1982, pp. 699-717.
[14] J. L. Kuhns, "Answering questions by computer: A logical study," Rand Corp., Tech. Rep. Rm-5428-PR, 1967.
[15] J. A. Makowsky, "Characterizing database dependencies," in8th Colloq. Automata, Languages and Programming. New York: Springer-Verlag, 1981.
[16] Z. Manna,Mathematical Theory of Computation. New York: McGraw-Hill, 1974.
[17] J.-M. Nicolas, "On the stability of relational queries," ONERACERT, Tech. Rep., 1982.
[18] J.-M. Nicolas, "Logic for improving integrity checking in relational databases,"Acta Inform., vol. 18, no. 3, pp. 227-253, 1982.
[19] G.Özsoyoglu, V. Matos, and Z.M.Özsoyoglu, "Query-Processing Techniques in the Summary-Table-by-Example Database Query Language,"ACM Trans. on Database Systems, Vol. 14, No. 4, Dec. 1989, pp. 526-573.
[20] G. Ozsoyoglu and V. Matos, "On optimizing summary-table-by-example queries," inProc. ACM PODS Conf., 1985.
[21] S. Osborn, private communication, Feb. 1987.
[22] Z. M. Ozsoyoglu and G. Ozsoyoglu, "A query language for statistical databases," inQuery Processing in Database Systems, W. Kim, D. Reiner, and D. Batory, Eds. New York: Springer-Verlag, 1985.
[23] Ozsoyoglu, Z.M., and G. Ozsoyoglu, "Summary-Table-By-Example: A Database Query Language for Manipulating Summary Data,"First IEEE Int'l Data Eng. Conf., IEEE CS Press, Los Alamitos, Calif., Order No. 533 (microfiche only), 1984, pp. 193- 202.
[24] A. Pirotte, "High level data base query languages," inLogic and Data Bases, H. Gallarie and J. Minker, Eds. New York: Plenum, 1978.
[25] A. U. Tansel, E. Arkun, and G. Ozsoyoglu, "Time-by-example query language for historical databases,"IEEE Trans. Software Eng., Apr. 1989.
[26] R. Topor, "Domain independent formulas and databases," Univ. Melbourne, Tech. Rep. 86/11, 1986 (to appear inTheoretical Comput. Sci.).
[27] J. D. Ullman,Principles of Databases Systems. Rockville, MD: Computer Science Press, 1982.
[28] M. M. Zloof, "Query-by-example: A data base language,"IBM Syst. J., 1977.

Index Terms:
algorithms; relational calculus; set operators; safety; graphical languages; set comparison; set manipulation; Codd relational calculus; RC/S queries; RC query; evaluable formulas; allowed formulas; RC/S* query; Query-by-Example; QBE; computer graphics; database theory; query languages; relational databases
G. Ozsoyoglu, H. Wang, "A Relational Calculus with Set Operators, Its Safety, and Equivalent Graphical Languages," IEEE Transactions on Software Engineering, vol. 15, no. 9, pp. 1038-1052, Sept. 1989, doi:10.1109/32.31363
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