Compositional Reasoning using Interval Temporal Logic and Tempura

  • B. C. Moszkowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1536)


We present a compositional methodology for specification and proof using Interval Temporal Logic (ITL). After given an introduction to ITL, we show how fixpoints of various ITL operators provide a flexible way to modularly reason about safety and liveness. In addition, some new techniques are described for compositionally transforming and refining ITL specifications. We also consider the use of ITL’s programming language subset Tempura as a tool for testing the kinds of specifications dealt with here.


Temporal Logic Inference Rule Proof System State Formula Proof Outline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dutertre, B.: On first order interval temporal logic. In: 10th Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, California (1995) 36–43Google Scholar
  2. 2.
    Francez, N., Pnueli, A.: A proof method for cyclic programs. Acta Inf. 9 (1978) 133–157zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Halpern J., Manna Z., Moszkowski B.: A hardware semantics based on temporal intervals. In: Diaz, J. Ed. Proceedings of the 10th International Colloquium on Automata, Languages and Programming (ICALP’83). Lecture Notes in Computer Science Vol. 154. Springer-Verlag, Berlin Heidelberg New York (1983) 278–291CrossRefGoogle Scholar
  4. 4.
    Hoare, C.A.R.: An axiomatic basis for computer programming. Comm. ACM 12 (1969) 576–580, 583zbMATHCrossRefGoogle Scholar
  5. 5.
    Jones, C.B.: Specification and design of (parallel) programs. In: Mason, R.E.A. Ed. Proceedings of Information Processing’ 83. North Holland Publishing Co., Amsterdam (1983) 321–332Google Scholar
  6. 6.
    Kesten, Y., Pnueli, A.: A complete proof system for QPTL. In: Proc. 10th IEEE Symp. on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, California (1995) 2–12Google Scholar
  7. 7.
    Kleene, S.C.: Mathematical Logic. John Wiley & Sons, Inc., New York (1967)zbMATHGoogle Scholar
  8. 8.
    Kono, S.: A combination of clausal and non clausal temporal logic programs. In: Fisher, M., Owens, R. Eds. Executable Modal and Temporal Logics. Lecture Notes in Computer Science, Vol. 897. Springer-Verlag, Berlin Heidelberg New York (1995) 40–57Google Scholar
  9. 9.
    Kröger, F.: Temporal Logic of Programs. Springer-Verlag, Berlin Heidelberg New York (1987)zbMATHGoogle Scholar
  10. 10.
    Manna, Z.: Verification of sequential programs: temporal axiomatization. In: Broy, M., Schmidt, G. Eds., Theoretical Foundations of Programming Methodology. D. Reidel Publishing Co. (1982) 53–102Google Scholar
  11. 11.
    Moszkowski B.: Reasoning about Digital Circuits. PhD thesis, Stanford University, Stanford, California (1983)Google Scholar
  12. 12.
    Moszkowski, B.: A temporal logic for multilevel reasoning about hardware. IEEE Computer 18 (1985) 10–19Google Scholar
  13. 13.
    Moszkowski, B.: Executing Temporal Logic Programs. Cambridge University Press, Cambridge, England (1986)Google Scholar
  14. 14.
    Moszkowski, B.: Some very compositional temporal properties. In: Olderog, E.-R. Ed. Programming Concepts, Methods and Calculi. IFIP Transactions, Vol. A-56, North-Holland (1994) 307–326.Google Scholar
  15. 15.
    Moszkowski, B.: Compositional reasoning about projected and infinite time. In: Proceedings of the First IEEE International Conference on Engineering of Complex Computer Systems (ICECCS’95). IEEE Computer Society Press, Los Alamitos, California (1995) 238–245CrossRefGoogle Scholar
  16. 16.
    Moszkowski, B.: Embedding imperative constructs in interval temporal logic. Internal memorandum EE/0895/M1. Dept. of Elec. and Elec. Eng., Univ. of Newcastle, Newcastle upon Type, UK (1995)Google Scholar
  17. 17.
    Moszkowski, B.: Using temporal fixpoints to compositionally reason about liveness. In: BCS-FACS 7th Refinement Workshop, “Electronic Workshops in Computing” series. Springer-Verlag, London (1996)Google Scholar
  18. 18.
    Paech, B.: Gentzen-systems for propositional temporal logics. In: Börger, E. et al. Eds. Proceedings of the 2nd Workshop on Computer Science Logic. Lecture Notes in Computer Science. Vol. 385. Springer-Verlag, Berlin Heidelberg New York (1988) 240–253Google Scholar
  19. 19.
    Rosner, R., Pnueli, A.: A choppy logic. In: Proceedings of the 1st Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, California (1986) 306–314.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • B. C. Moszkowski
    • 1
  1. 1.Department of Electrical and Electronic EngineeringUniversity of Newcastle upon TyneNewcastleGreat Britain

Personalised recommendations