Some extensions to propositional mean-value calculus: Expressiveness and decidability

  • Paritosh K. Pandya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1092)


Two extensions to the propositional mean-value calculus of Zhou and Li [27] are given. The first enriches the logic with outward looking modalities D1/D2 and D1/D2, and the second allows quantification over state varaibles in formulae. The usefulness of these extensions is demonstrated by some examples. The expressive power and decidability of the resulting logics are analysed. This analysis is achieved by reducing the decidability/expressiveness questions to the corresponding questions in the monadic theory of order [19].


Boolean Function Temporal Logic Expressive Power Predicate Symbol Propositional Variable 
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  1. 1.
    M. Abadi, L. Lamport: The existence of refinement mappings, Theoretical Computer Science, 82(2), 1991.Google Scholar
  2. 2.
    R. Alur, T.A. Henzinger: Logics and models of real time: a survey. In Real Time: Theory in Practice, Mook, The Netherlands, June 1991, LNCS 600, pp 74–106, 1992.Google Scholar
  3. 3.
    J.R. Buchi: Weak second order arithmetic and finite automata, Z. Math. Logik und Grundl. Math. 6, 1960.Google Scholar
  4. 4.
    J.P. Burgess: Basic tense logic, in Handbook of Philosophical Logic, Vol.2, D. Reidel Publ. Co., 1984.Google Scholar
  5. 5.
    A.K.Chandra, J. Halpern, A. Meyer, R. Parikh: Equations between regular terms and an application to process logic, in Proc. 13 ACM Symp. on Theory of Computing, 1991.Google Scholar
  6. 6.
    E.A. Emerson: Temporal and modal logics, in Handbook of Theo. Comp. Science, Vol. B, The MIT Press, Cambridge, 1990.Google Scholar
  7. 7.
    H.B. Enderton: A mathematical introduction to logic, Academic Press, 1972.Google Scholar
  8. 8.
    M.R. Hansen, E.R. Olderog et al: A Duration Calculus Semantics for Real-Time Reactive Systems, ProCoS-II Project Report OLD MRH 1/1, Universitat Oldenburg, Germany, 1993.Google Scholar
  9. 9.
    M.R. Hansen, Zhou Chaochen: Semantics and Completeness of Duration Calculus, J. W. de Bakker, C. Huizing, W.-P. de Roever, G. Rozenberg, (Eds) Real-Time: Theory in Practice, REX Workshop, LNCS 600, pp 209–225, 1992Google Scholar
  10. 10.
    M.R. Hansen, P.K. Pandya, Zhou Chaochen: Finite divergence, Theoretical Computer Science, 138 (1995).Google Scholar
  11. 11.
    J. Halpern, Y. Shoham: A prepositional modal logic of time intervals, JACM, 38(4), 1991.Google Scholar
  12. 12.
    Li Xiaoshan: A Mean-Value Duration Calculus, Ph.D. Thesis, Institute of Software, Academia Sinica, Beijing, September 1993.Google Scholar
  13. 13.
    B. Moszkowski: A Temporal Logic for Multi-level Reasoning about Hardware. In IEEE Computer, Vol. 18(2), pp10–19, 1985.Google Scholar
  14. 14.
    Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag, New York, 1991.Google Scholar
  15. 15.
    P.K. Pandya: Weak chop inverses and liveness in Mean-value Calculus, Technical Report TR-CS-95/2, Computer Science Group, TIFR, Bombay (August, 1994).Google Scholar
  16. 16.
    P.K. Pandya: A Recursive Mean Value Calculus, Technical Report TR-CS-95/3, Computer Science Group, TIFR, Bombay, (August 1994).Google Scholar
  17. 17.
    P.K. Pandya, Y.S. Ramakrishna, R.K. Shyamasundar: A Compositional Semantics of Esterel in Duration Calculus, in proc. Second AMAST workshop on Real-time systems: Models and Proofs, Bordeux, (June, 1995).Google Scholar
  18. 18.
    M.O. Rabin: Decidability of second order theories and automata on infinite trees, Trans. A.M.S. 149 (1969).Google Scholar
  19. 19.
    S. Shelah: Monadic Theory of Order, Annals of of Math., 102 (1975).Google Scholar
  20. 20.
    J.U. Skakkebaek: Liveness and Fairness in Duration Calculus, in Proc CON-CUR'94, LNCS 836, Springer-Verlag, 1994.Google Scholar
  21. 21.
    W. Thomas: Automata on infinite words, in Handbook of Theo. Comp. Science, Vol. B, The MIT Press, Cambridge, 1990.Google Scholar
  22. 22.
    Y. Venema: A modal logic for Chopping Intervals, Jour. Logic Computation, 1(4), 1991.Google Scholar
  23. 23.
    Zhou Chaochen: Duration Calculi: An Overview, in Formal methods in programming and their applications, D. Bjorner, M. Broy and I.V. Pottosin (Eds.), LNCS 735, 1993.Google Scholar
  24. 24.
    Zhou Chaochen, M.R. Hansen, A.P. Ravn, H. Rischel: Duration Specifications for Shared Processors, Proc. of the Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, Nijmegen, January 1992, LNCS 571, pp 21–32, 1992.Google Scholar
  25. 25.
    Zhou Chaochen, M.R. Hansen, P. Sestoft: Decidability and Undecidability Results for Duration Calculus, Proc. of STACS '93. 10th Symposium on Theoretical Aspects of Computer Science, Würzburg, Feb. 1993.Google Scholar
  26. 26.
    Zhou Chaochen, C.A.R. Hoare, A.P. Ravn: A Calculus of Durations. In Information Processing Letters 40(5), 1991, pp. 269–276.Google Scholar
  27. 27.
    Zhou Chaochen, Li Xiaoshan: A Mean-Value Duration Calculus, in A classical mind: Essays in honour of C A R Hoare, Prentice-Hall international series in computer science, Prentice-Hall International, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Paritosh K. Pandya
    • 1
  1. 1.Tata Institute of Fundamental ResearchBombayIndia

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