Skip to main content

Proving finite satisfiability of deductive databases

  • Conference paper
  • First Online:
CSL '87 (CSL 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 329))

Included in the following conference series:

Abstract

It is shown how certain refutation methods can be extended into semi-decision procedures that are complete for both unsatisfiability and finite satisfiability. The proposed extension is justified by a new characterization of finite satisfiability. This research was motivated by a database design problem: Deduction rules and integrity constraints in definite databases have to be finitely satisfiable.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

9. References

  1. Bayer, R. Query Evaluation and Recursion in Deductive Database Systems. Technical Report TUM-18503, Technical University of Munich, 1985.

    Google Scholar 

  2. Bry, F., Decker, H. and Manthey, R. A Uniform Approach to Constraint Satisfaction and Constraint Satisfiability in Deductive Databases. In Advanced in Database Technology — Proc. EDBT '88. Mar., 1988. Springer-Verlag, LNCS 303.

    Google Scholar 

  3. Beth, E.W. The Foundation of Mathematics. North Holland, Amsterdam, 1959. cited in [SMUL 68].

    Google Scholar 

  4. Bry, F. and Manthey, R. Checking Consistency of Database Constraints: A Logical Basis. In Proc. 12th Int. Conf. on Very Large Data Bases (VLDB '86). Aug. 25–28, 1986.

    Google Scholar 

  5. Dreben, B. and Goldfarb, W. The Decision Problem — Solvable Classes of Quantified Formulas. Addison-Wesley, Reading, Massachussetts, 1979.

    Google Scholar 

  6. Davis, M. and Putnam, H. A Computing Procedure for Quantification Theory. J. of the ACM 7(3), Jul., 1960.

    Google Scholar 

  7. Fagin, R. and Vardi M.Y. The Theory of Data Dependencies — An Overview. In Proc. of ICALP. 1984.

    Google Scholar 

  8. Gallaire, H., Minker, J. and Nicolas, J.-M. Logic and Databases: A Deductive Approach. ACM Computing Surveys 16(2), Jun., 1984.

    Google Scholar 

  9. Kuhns, J.L. Answering Questions by Computer — A Logical Study. Rand Memo RM 5428 PR, Rand Corp., Santa Monica, Calif., 1967.

    Google Scholar 

  10. Loveland, D. Automated Theorem Proving: A Logical Basis. North-Holland, Amsterdam, 1978.

    Google Scholar 

  11. Manthey, R. and Bry, F. A Hyperresolution Proof Procedure and its Implementation in Prolog. In Proc. 11th German Workshop on Artificial Intelligence (GWAI '87). Sep. 28–Oct. 2, 1987. Springer-Verlag, IF 152.

    Google Scholar 

  12. Manthey, R. and Bry, F. SATCHMO: A Theorem Prover Implemented in Prolog. In Proc. 9th Conf. on Automated Deduction (CADE '88). May 23–26, 1988. Springer-Verlag, LNCS.

    Google Scholar 

  13. Mendelson, E. Introduction to Mathematical Logic. Van Nostrand Reinhold, New York, 1969.

    Google Scholar 

  14. Nicolas, J.-M. and Gallaire, H. Database: Theory vs. Interpretation. In Logic and Databases. Plenum, New York, 1978.

    Google Scholar 

  15. Reiter, R. Towards a Logical Reconstruction of Relational Database Theory. In On Conceptual Modelling. Springer-Verlag, Berlin and New York, 1984.

    Google Scholar 

  16. Smullyan, R. First-Order Logic. Springer-Verlag, New York, 1968.

    Google Scholar 

  17. Trachtenbrot, B.A. Impossibility of an Algorithm for the Decision Problem in Finite Classes. Dokl. Acad. Nauk. SSSR 70, 1950. in Russian, translated into English in Amer. Soc. Trans., Series 2, 23, 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Egon Börger Hans Kleine Büning Michael M. Richter

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Bry, F., Manthey, R. (1988). Proving finite satisfiability of deductive databases. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '87. CSL 1987. Lecture Notes in Computer Science, vol 329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50241-6_28

Download citation

  • DOI: https://doi.org/10.1007/3-540-50241-6_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50241-8

  • Online ISBN: 978-3-540-45960-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics