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An Adequate First Order Interval Logic

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Compositionality: The Significant Difference (COMPOS 1997)

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Abstract

This paper introduces left and right neighbourhoods as primitive interval modalities to deFine other unary and binary modalities of intervals in a first order logic with interval length. A complete first order logic for the neighbourhood modalities is presented.

It is demonstrated how the logic can support formal specification and verification of liveness and fairness, and also of various notions of real analysis.

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References

  1. J.F. Allen. Towards a general theory of action and time. Articial Intelligence, 23:123–154, 1984.

    Article  MATH  Google Scholar 

  2. R. Alur, C. Courcoubetis, T. Henzinger, and P-H. Ho. Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In Hybrid Systems, R.L. Grossman, A. Nerode, A.P. Ravn and H. Rischel (Eds), pages 209–229. LNCS 736, Springer-Verlag, 1993.

    Google Scholar 

  3. R. Barua and Zhou Chaochen. Neighbourhood logics: NL and NL2. Technical report, UNU/IIST Report No. 120, UNU/IIST, International Institute for Software Technology, P.O. Box 3058, Macau, 1997.

    Google Scholar 

  4. B. Dutertre. Complete proof systems for first order interval temporal logic. In Tenth Annual IEEE Symp. on Logic in Computer Science, pages 36–43. IEEE Press, 1995.

    Google Scholar 

  5. Marcin Engel and Hans Rischel. Dagstuhl-seminar specification problem-a duration calculus solution. Technical report, Department of Computer Science, Technical University of Denmark-Private Communication, 1994.

    Google Scholar 

  6. J. Halpern, B. Moskowski, and Z. Manna. A hardware semantics based on temporal intervals. In ICALP’83, volume 154 of LNCS, pages 278–291. Springer-Verlag, 1983.

    Google Scholar 

  7. J.Y. Halpern and Y. Shoham. A propositional modal logic of time intervals. In Proceedings of the First IEEE Symposium on Logic in Computer Science, pages 279–292. IEEE Computer Society Press, 1986.

    Google Scholar 

  8. M.R. Hansen and Zhou Chaochen. Duration calculus: Logical foundations. Formal Aspects of Computing 9: 283–330, 1997.

    Article  MATH  Google Scholar 

  9. M.R. Hansen, Zhou Chaochen, and Jørgen Staunstrup. A real-time duration semantics for circuits. In TAU’92: 1992 Workshop on Timing Issues in the Specification and Synthesis of Digital Systems, Princeton Univ., NJ. ACM/SIGDA, 1992.

    Google Scholar 

  10. M.R. Hansen, P.K. Pandya, and Zhou Chaochen. Finite divergence. Theoretical Computer Science, 138:113–139, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  11. L. Lamport. Hybrid systems in tla+. In Hybrid Systems, R.L. Grossman, A. Nerode, A.P. Ravn and H. Rischel (Eds), pages 77–102. LNCS 736, Springer-Verlag, 1993.

    Google Scholar 

  12. Z. Manna and A. Pnueli. Verifying hybrid systems. In Hybrid Systems, R.L. Grossman, A. Nerode, A.P. Ravn and H. Rischel (Eds), pages 4–35. LNCS 736, Springer-Verlag, 1993.

    Google Scholar 

  13. B. Moszkowski. Compositional reasoning about projected and infinite time. In First IEEE Intl. Conf. on Engineering of Complex Computer Systems. IEEE press, 1995.

    Google Scholar 

  14. P.K. Pandya. Weak chop inverses and liveness in duration calculus. In B. Jonsson and J. Parrow, editors, Formal Techniques in Real-Time and Fault-Tolerant Systems, pages 148–167. Springer-Verlag, 1996.

    Google Scholar 

  15. Suman Roy and Zhou Chaochen. Notes on neighbourhood logic. Technical report, UNU/IIST Report No. 97, UNU/IIST, International Institute for Software Technology, P.O. Box 3058, Macau, 1997.

    Google Scholar 

  16. J.U. Skakkebæk. Liveness and fairness in duration calculus. In B. Jonsson and J. Parrow, editors, CONCUR’94: Concurrency Theory, volume 836 of LNCS, pages 283–298. Springer Verlag, 1994.

    Chapter  Google Scholar 

  17. Y. Venema. Expressiveness and completeness of an interval tense logic. Notre Dame Journal of Formal Logic, 31(4):529–547, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  18. Y. Venema. A modal logic for chopping intervals. J. Logic Computat., 1(4):453–476, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  19. Mao Xiaoguang, Xu Qiwen, Dang Van Hung, and Wang Ji. Towards a proof assistant for interval logics. Technical report, UNU/IIST Report No. 77, UNU/IIST, International Institute for Software Technology, P.O. Box 3058, Macau, 1996.

    Google Scholar 

  20. Zhou Chaochen and Michael R. Hansen. Chopping a point. In BCS-FACS 7th Refinement Workshop. Electronic Workshops in Computing, Springer-Verlag, 1996.

    Google Scholar 

  21. Zhou Chaochen, C.A.R. Hoare, and A.P. Ravn. A calculus of durations. Information Processing Letters, 40(5):269–276, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  22. Zhou Chaochen, Dang Van Hung, and Li Xiaoshan. A duration calculus with infinite intervals. In Horst Reichel, editor, Fundamentals of Computation Theory, volume 965 of LNCS, pages 16–41. Springer-Verlag, 1995.

    Google Scholar 

  23. Zhou Chaochen, A.P. Ravn, and M.R. Hansen. An extended duration calculus for hybrid systems. In R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel, editors, Hybrid Systems, R.L. Grossman, A. Nerode, A.P. Ravn, H. Rischel (Eds.), volume 736 of LNCS, pages 36–59. Springer-Verlag, 1993.

    Google Scholar 

  24. Zhou Chaochen and Li Xiaoshan. A mean value calculus of durations. In Prentice Hall International, editor, A Classical Mind: Essays in Honour of C.A.R. Hoare, pages 431–451. Prentice Hall International, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. UNU/IIST, P.O.Box 3058, Macau

    Zhou Chaochen

  2. Department of Information Technology, Technical University of Denmark, DK-2800, Lyngby

    Michael R. Hansen

Authors
  1. Zhou Chaochen
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  2. Michael R. Hansen
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Editor information

Editors and Affiliations

  1. Department of Informatics and Applied Mathematics, Christian Albrechts University at Kiel, Preußerstr. 1-9, D-24105, Kiel, Germany

    Willem-Paul de Roever  & Hans Langmaack  & 

  2. Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, P.O. Box 26, Rehovot, 76100, Israel

    Amir Pnueli

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© 1998 Springer-Verlag Berlin Heidelberg

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Chaochen, Z., Hansen, M.R. (1998). An Adequate First Order Interval Logic. In: de Roever, WP., Langmaack, H., Pnueli, A. (eds) Compositionality: The Significant Difference. COMPOS 1997. Lecture Notes in Computer Science, vol 1536. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49213-5_23

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  • DOI: https://doi.org/10.1007/3-540-49213-5_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65493-3

  • Online ISBN: 978-3-540-49213-9

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