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A time-interval calculus

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Mathematics of Program Construction (MPC 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 669))

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Abstract

The purpose of this paper is to introduce a notation for expressing the requirements of time-critical systems and a calculus for reasoning about them. The Actions, Events and States of a system are represented by sets of time intervals for which they hold. Firstly the timing model is introduced and the calculus is compared with Tarski's calculus of relations. Then states and duration are introduced and a case study is provided. Finally the connection with the duration calculus and other temporal logics is shown.

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References

  1. H. Barringer:. Up and Down The Temporal Way. The Computer Journal, 30:2 pp 143–148 (1987).

    Google Scholar 

  2. J. van Bentham:. Time, Logic and Computation. G. Rozenberg, ed, REX Workshop on Temporal logic and Concurrency, Springer, 1988.

    Google Scholar 

  3. S. M. Brien:. A Relational Calculus of Intervals. MSc Thesis, PRG Oxford Univ. Comp. Lab., Sep 1990.

    Google Scholar 

  4. Z. Chaochen, M. R. Hansen:. A note on completeness of the duration Calculus. ProCos Note, 1991.

    Google Scholar 

  5. Z. Chaochen, C. A. R. Hoare, A. P. Ravn:. A Calculus of Durations. PRG Oxford Univ. Comp. Lab., Feb 1991.

    Google Scholar 

  6. B. A. Davey, H. A. Priestley:. An introduction to Lattices and Order. Cambridge University Press, 1990.

    Google Scholar 

  7. E. W. Dijkstra:. A Relational Summary. EWD 1047, Austin TX, Nov 1990.

    Google Scholar 

  8. E. W. Dijkstra, C.S. Scholten:. Predicate Calculus and Program Semantics. Springer Verlag, 1990.

    Google Scholar 

  9. R. W. S. Hale:. Programming in Temporal Logic. PhD Thesis, Univ. Cambridge, Oct 1988.

    Google Scholar 

  10. C. A. R. Hoare, He Jifeng:. The Weakest Prespecification. Oxford Univ. Comp. Lab, Technical Monograph PRG-44, 1985.

    Google Scholar 

  11. G. E. Hughes, M. J. Creswell:. An Introduction to Modal Logic. Methuen, 1968.

    Google Scholar 

  12. G. E. Hughes, M. J. Creswell:. An Companion to Modal Logic. Methuen, 1984.

    Google Scholar 

  13. F. Jahanian, A. K-L. Mok:. Safety Analysis of Timing Properties in Real-Time Systems. IEEE Trans. SE, Vol. SE-12(9), pp 890–904 (1986).

    Google Scholar 

  14. K. M. Jensen:. Specification of a Lift Control System. ProCoS report: ID/DTH KMJ 12/1 (1990).

    Google Scholar 

  15. R. Koymans:. Specifying Message Passing and Time-Critical Systems with Temporal Logic. Phd Thesis, Eindhoven, 1989

    Google Scholar 

  16. R. Koymans:. Specifying Real-Time Properties with Metric Temporal Logic. Real-time Systems, 2, pp 255–299 (1990).

    Google Scholar 

  17. M. Moszkowski, Z. Manna:. Reasoning in Interval Temporal logic. LNCS 164, Logics of Programs, pp 371–382, 1983.

    Google Scholar 

  18. N. Rescher, A. Urquhart:. Temporal Logic. Springer-Verlag, 1971.

    Google Scholar 

  19. S. Rossig:. Trace oriented specification of a single lift system. ProCoS Technical Report OLD SR 4/1, 1990.

    Google Scholar 

  20. A. Tarski:. On the Calculus of Relations. Journal of Symbolic Logic, 6:3, pp 73–88 (1941).

    Google Scholar 

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Authors and Affiliations

  1. Programming Research Group, Oxford University Computing Laboratory, 8-1 Keble Road, OX1 3QD, Oxford

    S. M. Brien

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  1. S. M. Brien
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Editor information

R. S. Bird C. C. Morgan J. C. P. Woodcock

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© 1993 Springer-Verlag Berlin Heidelberg

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Brien, S.M. (1993). A time-interval calculus. In: Bird, R.S., Morgan, C.C., Woodcock, J.C.P. (eds) Mathematics of Program Construction. MPC 1992. Lecture Notes in Computer Science, vol 669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56625-2_8

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  • DOI: https://doi.org/10.1007/3-540-56625-2_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56625-0

  • Online ISBN: 978-3-540-47613-9

  • eBook Packages: Springer Book Archive

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