Skip to main content
SpringerLink
Log in

Semantic Classifications of Queries to Relational Databases

  • Conference paper
  • First Online:
Semantics in Databases (SiD 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2582))

Included in the following conference series:

Abstract

We survey different semantic classifications of queries to relational databases, as well as the different systems of partial isomorphisms developed as algebraic (hence, semantic) characterizations of equality of theories for databases, in FO and in weaker logics. We introduce an abstract notion of similarity for databases, as equality in the theories for a given logic and we define different sub-classes of queries by requiring that the queries in a given sub-class should not distinguish between databases which are similar. Then we use this general strategy to present a new semantic classification, with the class of bounded variable logics with counting (C k), as the target logics. One important consequence of the definition of the two semantic classifications of queries which we present here is their orthogonality with the TIME-SPACE hierarchy defined in Turing machine complexity, allowing the definition of finer complexity classes by intersecting orthogonal hierarchies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abiteboul, S., Hull, R. and Vianu, V.: Foundations of Databases. Addison-Wesley (1994)

    Google Scholar 

  2. Abiteboul, S., Papadimitriou, C. and Vianu, V.: Reflective Relational Machines. Information and Computation 143 (1998) 110–136

    Article  MATH  MathSciNet  Google Scholar 

  3. Abiteboul, S. and Vianu, V.: Computing with first-order logic. Journal of Computer and System Sciences 50(2) (1995) 309–335

    Article  MATH  MathSciNet  Google Scholar 

  4. Abiteboul, S., Vardi, M. and Vianu, V.: Computing with Infinitary Logic. Theoretical Computer Science 149(1) (1995) 101–128

    Article  MATH  MathSciNet  Google Scholar 

  5. Abiteboul, S., Vardi, M. and Vianu, V.: Fixpoint Logics, Relational Machines, and Computational Complexity. Journal of ACM 44(1) (1997) 30–56

    Article  MATH  MathSciNet  Google Scholar 

  6. Barwise, J.: On Moschovakis Closure Ordinals. Journal of Symbolic Logic 42 (1977) 292–296

    Article  MATH  MathSciNet  Google Scholar 

  7. Balcázar, J., Díaz, J., Gabarró, J.: Structural Complexity I, 2nd ed. Springer (1995)

    Google Scholar 

  8. Babai, L., Erdös, P. and Selkow, S.: Random Graph Isomorphism. SIAM Journal on Computing 9 (1980) 628–635

    Article  MATH  MathSciNet  Google Scholar 

  9. Cai, J. Y., Fürer, M. and Immerman, N.: An Optimal Lower Bound on the Number of Variables for Graph Identification. Combinatorica 12(4) (1992) 389–410

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Chang, C. and Keisler, H.: Model Theory, 3rd ed. Elsevier North Holland (1992)

    Google Scholar 

  12. Denenberg, L., Gurevich, Y., Shelah, S.: Definability by Constant Depth Polinomial Size Circuits. Information and Control 70 (1986) 216–240

    Article  MATH  MathSciNet  Google Scholar 

  13. Ebbinghaus, H. and Flum, J.: Finite Model Theory, 2nd ed. Springer (1999)

    Google Scholar 

  14. Ebbinghaus, H., Flum, J., Thomas, W.: Mathematical Logic. Springer (1984)

    Google Scholar 

  15. Ehrenfeucht, A.: An Application of Games to the Completeness Problem for Formalized Theories. Fundamenta Mathematicae 49 (1961) 129–141

    MATH  MathSciNet  Google Scholar 

  16. Fagin, R.: Probabilities on Finite Models. Journal of Symbolic Logic 41 (1976) 50–58

    Article  MATH  MathSciNet  Google Scholar 

  17. Fraïssé, R.: Sur Quelques Classifications des Systèmes de Relations (english summary). Université d’Alger, Publications Scientifiques, Série A 1 (1954) 35–182

    Google Scholar 

  18. Glebskij, Y. V., Kogan, D. I., Liogon'kij, M. I., Talanov, V. A.: Range and Degree of Realizability of Formulas in the Restricted Predicate Calculus. Cybernetics 5 (1969) 142–154

    Article  Google Scholar 

  19. Grohe, M.: Equivalence in Finite Variable Logics is Complete for Polynomial Time. Proc. of 37th IEEE Symposium on Foundations of Computer Science (1996) 264–273

    Google Scholar 

  20. Grohe, M.: Finite Variable Logics in Descriptive Complexity Theory. Preliminary version (1998)

    Google Scholar 

  21. Grohe, M.: Fixed Point Logics on Planar Graphs. Proc. of 13th IEEE Symposium on Logic in Computer Science (1998) 6–15

    Google Scholar 

  22. Hella, L.: Logical Hierarchies in PTIME. Information and Computation 129(1) (1996) 1–19

    Article  MATH  MathSciNet  Google Scholar 

  23. Hella, L., Kolaitis, P. and Luosto, K.: Almost Everywhere Equivalence of Logics in Finite Model Theory. The Bulletin of Symbolic Logic 2(4) (1996) 422–443

    Article  MATH  MathSciNet  Google Scholar 

  24. Immerman, N. and Lander, E.: Describing Graphs: A First Order Approach to Graph Canonization. Complexity Theory Retrospective, A. Selman, ed. Springer (1990) 59–81

    Google Scholar 

  25. Immerman, N.: Upper and Lower Bounds for First Order Expressibility. Journal of Computer and System Sciences 25(1) (1982) 76–98

    Article  MATH  MathSciNet  Google Scholar 

  26. Immerman, N.: Descriptive Complexity. Springer (1999)

    Google Scholar 

  27. Koponen, A. and Luosto, K.: Definability of Group Theoretic notions. Research Report 227 of the Department of Mathematics of the University of Helsinki (1999)

    Google Scholar 

  28. Koponen, A. and Luosto, K.: personal comunication (2000)

    Google Scholar 

  29. Kolaitis, P., Vardi, M.: On the Expressive Power of Datalog: Tools and a Case Study. Proceedings of the 9th ACM Symposium on Principles of Database Systems (1990) 61–71

    Google Scholar 

  30. Kolaitis, P. and Vardi, M.: Infinitary Logic and 0-1 Laws. Information and Computation 98 (1992) 258–294

    Article  MATH  MathSciNet  Google Scholar 

  31. Otto, M.: Symmetry and First Order: Explicitly Presentation-Invariant Circuits. Preliminary report (1994)

    Google Scholar 

  32. Otto, M.: The Expressive Power of Fixed Point Logic with Counting. Journal of Symbolic Logic 61, 1 (1996) 147–176

    Article  MATH  MathSciNet  Google Scholar 

  33. Otto, M.: Bounded Variable Logics and Counting. Springer (1997)

    Google Scholar 

  34. Poizat, B.: Deux ou trois choses que je sais de Ltnn. Journal of Symbolic Logic 47 (1982) 641–658

    Article  MATH  MathSciNet  Google Scholar 

  35. Rosen, E., Weinstein, S.: Preservation Theorems in Finite Model Theory. Proceedings of the International Workshop on Logic and Computational Complexity, Springer LNCS 960 (1994) 480–502

    Google Scholar 

  36. Turull Torres, J.M.: Untyped Queries, Untyped Reflective Machines and Conditional Quantifiers. Proceedings of the 2nd East European Symposium on Advances in Database and Information Systems, ADBIS’98, Springer, LNCS 1475 (1998) 35–45

    Google Scholar 

  37. Turull Torres, J.M.: Reflective Relational Machines Working on Homogeneous Databases. Proceedings of the First International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2000, Springer, LNCS 1762 (2000) 288–303

    Google Scholar 

  38. Turull Torres, J.M.: On the Expressibility and the Computability of Untyped Queries. Annals of Pure and Applied Logic 108 (2001) 345–371

    Article  MATH  MathSciNet  Google Scholar 

  39. Turull Torres, J. M.: A Study of Homogeneity in Relational Databases. To appear in Annals of Mathematics and Artificial Intelligence (2001)

    Google Scholar 

  40. Turull Torres, J.M.: Relational Databases and Homogeneity in Logics with Counting. Draft (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Systems, Massey University Information Science Research Centre, PO Box 756, Wellington, New Zealand

    José María Turull Torres

Authors
  1. José María Turull Torres
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, Herzberg Building, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Leopoldo Bertossi

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364, Budapest, Hungary

    Gyula O. H. Katona

  3. Department of Information Systems, Massey University, Private Bag 11222, Palmerston North, New Zealand

    Klaus-Dieter Schewe

  4. Institute of Computer Science, Brandenburg University of Technology at Cottbus, P.O. Box 10 13 44, 03013, Cottbus, Germany

    Bernhard Thalheim

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Torres, J.M.T. (2003). Semantic Classifications of Queries to Relational Databases. In: Bertossi, L., Katona, G.O.H., Schewe, KD., Thalheim, B. (eds) Semantics in Databases. SiD 2001. Lecture Notes in Computer Science, vol 2582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36596-6_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-36596-6_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00957-3

  • Online ISBN: 978-3-540-36596-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation