Skip to main content
SpringerLink
Log in
Book cover

European Workshop on Logics in Artificial Intelligence

JELIA 1992: Logics in AI pp 65–83Cite as

Weak implication: Theory and applications

  • Conference paper
  • First Online:

  • 278 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 633))

Abstract

We study a generalization of the classical notion of implication, called weak implication. It extends unquantified predicate logic with a single level of existential quantification. We present a sound and complete set of deduction rules for weak implications.

The notion of weak implication was introduced for the sake of a formal specification of a symbolic constraint solving system. Other practical applications of can be found in the realm of relational database theory: query normalization and integrity constraints in the context of views.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W.F. Clocksin & C.S. Mellish. Programming in Prolog. Springer-Verlag, 1981.

    Google Scholar 

  2. S. van Denneheuvel. Constraint solving on database systems. Design and implementation of the rule language RL/1. Thesis. University of Amsterdam, 1991.

    Google Scholar 

  3. S. v Denneheuvel & K.L. Kwast. Weak equivalence for constraint solving. In: Proceedings of IJCAI'91: Int. Joint Conference on A.I. Sydney. Morgan Kaufmann, 1991.

    Google Scholar 

  4. S. v Denneheuvel, G.R. Renardel de Lavalette, E. Spaan & K.L. Kwast. Query optimization using rewrite rules. In: R. Book (ed.), Proceedings of RTA'91: Int. Conference on Rewriting Techniques and Applications. Como, LNCS488, 1991.

    Google Scholar 

  5. J. Jaffar & S. Michaylov. Methodology and Implementation of a CLP System. In: J-L. Lassez (ed.), Proceedings of the 4th Int. Conference on Logic Programming, MIT Press, 1987.

    Google Scholar 

  6. K.L. Kwast. Unknown values in the relational database system. Thesis. University of Amsterdam, 1992.

    Google Scholar 

  7. J.H. Siekmann. Unification Theory. In: Journal of Symbolic Computation, Vol. 7, 1989.

    Google Scholar 

  8. J.D. Ullman. Principles of Data and Knowledge-Base Systems, Vol. I & II. Computer Science Press, 1989.

    Google Scholar 

  9. S. Wolfram. Mathematica, a System for Doing Math by Computer. Addison-Wesley, 1988.

    Google Scholar 

  10. H.Z. Yang & P.A. Larson. Query Transformation for PSJ-queries. In: Proceedings of the 13th VLDB: Int. Conference on Very Large Databases, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics & Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam

    Karen L. Kwast & Sieger van Denneheuvel

Authors
  1. Karen L. Kwast
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sieger van Denneheuvel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

D. Pearce G. Wagner

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kwast, K.L., van Denneheuvel, S. (1992). Weak implication: Theory and applications. In: Pearce, D., Wagner, G. (eds) Logics in AI. JELIA 1992. Lecture Notes in Computer Science, vol 633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023422

Download citation

  • DOI: https://doi.org/10.1007/BFb0023422

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55887-3

  • Online ISBN: 978-3-540-47304-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation