Nothing Special   »   [go: up one dir, main page]

Skip to main content

Axiomatizing U and S over integer time

  • Conference paper
  • First Online:
Temporal Logic (ICTL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 827))

Included in the following conference series:

  • 167 Accesses

Abstract

We give a Hilbert style axiomatization for the set of formulas in the temporal language with Until and Since which are valid over the integer number flow of time. We prove weak completeness for this orthodox axiom system.

The author would like to thank the temporal logic group at Imperial College for suggesting many improvements. The work was supported by the U.K. Science and Engineering Research Council under the Metatem project (GR/F/28526).

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.

References

  1. J P Burgess. Axioms for tense logic I: “since” and “until”. Notre Dame J Formal Logic, 23(2):367–374, 1982.

    Google Scholar 

  2. Marcelo Finger. Handling database updates in two-dimensional temporal logic. J. of Applied Non-Classical Logic, pages 201–224, 1992.

    Google Scholar 

  3. D M Gabbay and I M Hodkinson. An axiomatisation of the temporal logic with until and since over the real numbers. Journal of Logic and Computation, 1(2):229–260, 1990.

    Google Scholar 

  4. D.M. Gabbay, A. Pnueli, S. Shelah, and J. Stavi. On the temporal analysis of fairness. In 7th ACM Symposium on Principles of Programming Languages, Las Vegas, pages 163–173, 1980.

    Google Scholar 

  5. D M Gabbay, I M Hodkinson, and M A Reynolds. Temporal expressive completeness in the presence of gaps. In Proceedings ASL European Meeting 1990, Lecture Notes in Logic. Springer-Verlag, 1993.

    Google Scholar 

  6. D Gabbay, I Hodkinson, and M Reynolds. Temporal Logic: Mathematical Foundations and Computational Aspects, Vol. 1. OUP, to appear 1994.

    Google Scholar 

  7. D M Gabbay. An irreflexivity lemma with applications to aximatizations of conditions on tense frames. In U Monnich, editor, Aspects of Philosophical Logic, pages 67–89. Reidel, Dordrecht, 1981.

    Google Scholar 

  8. J Kamp. Tense Logic and the theory of linear order. PhD thesis, Michigan State University, 1968.

    Google Scholar 

  9. M Reynolds. An axiomatization for Until and Since over the reals without the IRR rule. Studia Logica, 51:165–194, 1992.

    Article  Google Scholar 

  10. J G Rosenstein. Linear orderings. Academic Press, New York, 1982.

    Google Scholar 

  11. J van Bentham. The Logic of Time. Reidel, Dordrecht, 1983.

    Google Scholar 

  12. Y Venema. Completeness via completeness. In M de Rijke, editor, Colloquium on Modal Logic, 1991. ITLI-Network Publication, Instit. for Lang., Logic and Information, University of Amsterdam, 1991.

    Google Scholar 

  13. Ming Xu. On some U,S-Tense Logics. Journal of Philosophical Logic, 17:181–202, 1988.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Dov M. Gabbay Hans Jürgen Ohlbach

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reynolds, M. (1994). Axiomatizing U and S over integer time. In: Gabbay, D.M., Ohlbach, H.J. (eds) Temporal Logic. ICTL 1994. Lecture Notes in Computer Science, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013984

Download citation

  • DOI: https://doi.org/10.1007/BFb0013984

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58241-0

  • Online ISBN: 978-3-540-48585-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics