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First-order definability over constraint databases

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Principles and Practice of Constraint Programming — CP '95 (CP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 976))

Abstract

In this paper, we study the expressive power of first-order logic as a query language over constraint databases. We consider constraints over various domains (ℕ,2e, ℝ), and with various operations (⩽, +, ×, x y). We first tackle the problem of the definability of parity and connectivity, which are the most classical examples of queries not expressible in first-order logic over finite structures. We prove that these two queries are first-order expressible in presence of (enough) arithmetic. This is in sharp contrast with classical relational databases. Nevertheless, we show that they are not definable with constraints of interest for constraint databases such as linear constraints. We then develop reductions techniques for queries over constraint databases, that allow us to draw conclusions with respect to their undefinability in various constraint query languages.

Work supported in part by Esprit Project BRA AMUSING, and an NSERC fellowship in Canada.

Work supported in part by NSF grant IRI-9117094 and NASA grant NAGW-3888. A part of this work was done while visiting I.N.R.I.A.

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References

  1. F. Afrati, S. Cosmadakis, S. Grumbach, and G. Kuper. Expressiveness of linear vs. polynomial constraints in database query languages. In Second Workshop on the Principles and Practice of Constraint Programming, 1994.

    Google Scholar 

  2. S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1994.

    Google Scholar 

  3. A. Chandra and D. Harel. Computable Queries for Relational Data Bases. Journal of Computer and System Sciences, 21(2):156–178, Oct. 1980.

    Article  Google Scholar 

  4. J. Chomicki and G. Kuper. Measuring infinite relations. In Proc. 14th ACM Symp. on Principles of Database Systems, San Jose, May 1995.

    Google Scholar 

  5. E.F. Codd. A relational model of data for large shared data banks. Communications of ACM, 13:6:377–387, 1970.

    Article  Google Scholar 

  6. A. K. Chandra, L. Stockmeyer, and U. Vishkin. Constant depth reducibility. SIAM J. on Computing, 13(2):423–439, May 1984.

    Article  Google Scholar 

  7. A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fund. Math, 49, 1961.

    Google Scholar 

  8. H. Enderton. A Mathematical Introduction to Logic. Academic Press, 1972.

    Google Scholar 

  9. R. Fagin. Generalized first-order spectra and polynomial-time recognizable sets. Complexity of Computations, SIAM-AMS Proceedings 7, pages 43–73, 1974.

    Google Scholar 

  10. R. Fagin. Finite model theory — a personal perspective. Theoretical Computer Science, 116:3–31, 1993.

    Article  Google Scholar 

  11. R. Fraïssé. Sur les classifications des systèmes de relations. Publ. Sci. Univ Alger, I:1, 1954.

    Google Scholar 

  12. M. Furst, J. B. Saxe, and M. Sipser. Parity, circuits, and the polynomialtime hierarchy. Mathematical System Theory, 17:13–27, 1984.

    Article  Google Scholar 

  13. H. Gaifman. On local and non local properties. In J. Stern, editor, Proc. Herbrand Symposium Logic Colloquium, pages 105–135. North Holland, 1981.

    Google Scholar 

  14. S. Grumbach and J. Su. Finitely representable databases. In 13th ACM Symp. on Principles of Database Systems, pages 289–300, Minneapolis, May 1994.

    Google Scholar 

  15. S. Grumbach and J. Su. Dense order constraint databases. In Proc. 14th ACM Symp. on Principles of Database Systems, San Jose, May 1995.

    Google Scholar 

  16. S. Grumbach, J. Su, and C. Tollu. Linear constraint databases. In D. Leivant, editor, Logic and Computational Complexity Workshop, Indianapolis, 1994. Springer Verlag. to appear in LNCS.

    Google Scholar 

  17. Y. Gurevich. Current Trends in Theoretical Computer Science, E. Borger Ed., chapter Logic and the Challenge of Computer Science, pages 1–57. Computer Science Press, 1988.

    Google Scholar 

  18. N. Immerman. Languages that capture complexity classes. SIAM J. of Computing, 16(4):760–778, Aug 1987.

    Article  Google Scholar 

  19. P. Kanellakis and D. Goldin. Constraint programming and database query languages. In Manuscript, 1994.

    Google Scholar 

  20. P. Kanellakis, G Kuper, and P. Revesz. Constraint query languages. In Proc. 9th ACM Symp. on Principles of Database Systems, pages 299–313, Nashville, 1990.

    Google Scholar 

  21. G.M. Kuper. Aggregation in constraint databases. In Proc. First Workshop on Principles and Practice of Constraint Programming, 1993.

    Google Scholar 

  22. J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proc. 13th ACM Symp. on Principles of Database Systems, pages 279–288, 1994.

    Google Scholar 

  23. J. Paredaens, J. Van den Bussche, and D. Van Gucht. First-order queries on finite structures over the reals. In Proc. IEEE Symposium on Logic In Computer Science, 1995.

    Google Scholar 

  24. P. Revesz. A closed form for datalog queries with integer (gap)-order constraints. Theoretical Computer Science, 116(1):117–149, 1993.

    Article  Google Scholar 

  25. P. Revesz. Datalog queries of set constraint databases. In Proc. Int. Conf. on Database Theory, 1995.

    Google Scholar 

  26. J. Robinson. Decidability and decision problems in arithmetic. Journal of Symbolic Logic, 14:98–114, 1949.

    Google Scholar 

  27. A. Tarski. A Decision method for elementary algebra and geometry. Univ. of California Press, Berkeley, California, 1951.

    Google Scholar 

  28. F.F. Yao. Handbook of Theorical Computer Science, volume A, chapter 7 Computational Geometry, pages 343–389. J. Van Leeuwen, North Holland, 1990.

    Google Scholar 

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Author information

Authors and Affiliations

  1. I.N.R.I.A. Rocquencourt, I.N.R.I.A. and University of Toronto, BP 105, 78153, Le Chesnay, France

    Stéphane Grumbach

  2. Dept. of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Jianwen Su

Authors
  1. Stéphane Grumbach
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  2. Jianwen Su
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Editor information

Ugo Montanari Francesca Rossi

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© 1995 Springer-Verlag Berlin Heidelberg

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Grumbach, S., Su, J. (1995). First-order definability over constraint databases. In: Montanari, U., Rossi, F. (eds) Principles and Practice of Constraint Programming — CP '95. CP 1995. Lecture Notes in Computer Science, vol 976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60299-2_8

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  • DOI: https://doi.org/10.1007/3-540-60299-2_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60299-6

  • Online ISBN: 978-3-540-44788-7

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