Skip to main content
SpringerLink
Log in

Untyped queries, untyped reflective machines and conditional quantifiers

  • Regular Papers
  • Conference paper
  • First Online:
Advances in Databases and Information Systems (ADBIS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1475))

Abstract

In the definition of the class CQ of computable queries, Chandra and Harel ([7]) included untyped queries, that is, queries whose answers are relations of possibly different arities on different databases. However, it seems that in the work which followed on the subject, untyped queries were not considered at all, neither in the abstract machines side nor in the logic framework. We propose to re-introduce these queries in the study of Query Computability, and also in the construction of Industry query languages, without leaving the Relational Model. So, we define an extension of the Reflective Relational Machine of [2], which we call untyped Reflective Relational Machine. In the logic framework, we define a new quantifier, which we call conditional quantifier, and we build with it an infinitary logic which we denote by \(\mathcal{L}_{\omega _1 \omega }^c\). Then we prove completeness results regarding both formalisms considering both typed and untyped queries.

The work presented here was done during a visit to the Department of Mathematics of the University of Helsinki.

This work has been partially supported by Grant 1011049 of the Academy of Finland and by a Grant of Universidad CAECE, Argentina.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abiteboul, S., Hull, R. Vianu, V.: Foundations of Databases. Addison-Wesley (1995)

    Google Scholar 

  2. Abiteboul, S., Papadimitriou, C. and Vianu, V.: The Power of the Reflective Relational Machine. Proc. of 9th IEEE Symposium on Logic in Computer Science (1994)

    Google Scholar 

  3. Abiteboul, S. and Vianu, V.: Generic Computation and its Complexity. Proc. of 23th ACM Symposium on Theory of Computing (1991) 209–219

    Google Scholar 

  4. Abiteboul, S., Vardi, M. and Vianu, V.: Fixpoint Logics, Relational Machines, and Computational Complexity. Proc. of 7th IEEE Conference on Structure in Complexity Theory (1992) 156–168

    Google Scholar 

  5. Abiteboul, S., Vardi, M. and Vianu, V.: Computing with Infinitary Logic. Proc. of International Conference on Database Theory (1992)

    Google Scholar 

  6. Balcázar, J., Díaz, J., Gabarró, J.: Structural Complexity II. Springer Verlag (1990)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Davis, M. and Weyuker, E.: Computability, Complexity and Languages. Corrected printing, Academic Press (1983)

    Google Scholar 

  9. Ebbinghaus, H., Flum, J.: Finite Model Theory. Springer Verlag (1995)

    Google Scholar 

  10. Grädel, E., Gurevich, Y.: Meta Finite Model Theory. To appear in Information and Computation. Preliminary version in Logic and Computational Complexity, International Workshop LCC’94, USA (1995)

    Google Scholar 

  11. Gurevich, Y.: Toward Logic Tailored for Computational Complexity. Computation and Proof Theory. Lecture Notes in Mathematics, Vol 1104. Springer-Verlag (1984) 175–216

    Google Scholar 

  12. Immerman, N.: Relational Queries Computable in Polynomial Time. Information and Control 68 (1986) 86–104

    Article  MATH  MathSciNet  Google Scholar 

  13. Kanellakis, P.: Elements of Relational Database Theory. Handbook of Theoretical Computer Science, Volume B. Elsevier and The MIT Press (1990) 1073–1156

    Google Scholar 

  14. Turull Torres, J.M.: Query Completeness, Distinguishability and Relational Machines. Proc. of the X Latin American Symposium on Mathematical Logic, Bogotá (1995)

    Google Scholar 

  15. Turull Torres, J.M.: Untyped Queries, Untyped Reflective Machines and Conditional Quantifiers. Research Report 146 of the Department of Mathematics of the University of Helsinki (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad National de San Luis Universidad Tecnológica National, F.R.B.A., Peron 2315, piso 4, depto. P, 1040, Capital Federal, Argentina

    Jose Maria Turull Torres

Authors
  1. Jose Maria Turull Torres
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Witold Litwin Tadeusz Morzy Gottfried Vossen

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Turull Torres, J.M. (1998). Untyped queries, untyped reflective machines and conditional quantifiers. In: Litwin, W., Morzy, T., Vossen, G. (eds) Advances in Databases and Information Systems. ADBIS 1998. Lecture Notes in Computer Science, vol 1475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057715

Download citation

  • DOI: https://doi.org/10.1007/BFb0057715

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64924-3

  • Online ISBN: 978-3-540-68309-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation