Annotation-based deduction in temporal logic

  • Hugh McGuire
  • Zohar Manna
  • Richard Waldinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 827)


This paper presents a deductive system for predicate temporal logic with induction.

Representing temporal operators by first-order expressions enables temporal deduction to use the already developed techniques of first-order deduction. But when translating from temporal logic to first-order logic is done indiscriminately, the ensuing quantifications and comparisons of time expressions encumber formulas, hindering deduction. So in the deductive system presented here, translation occurs more carefully, via reification rules. These rules paraphrase selected temporal formulas as nontemporal first-order formulas with time annotations. This time reification process suppresses quantifications (the process is analogous to quantifier skolemization) and uses addition instead of complicated combinations of comparisons. Some ordering conditions on arithmetic expressions can arise, but such are handled automatically by a special-purpose unification algorithm plus a decision procedure for Presburger arithmetic.

This deductive system is relatively complete.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AM90]
    Abadi, M., and Manna, Z.: “Nonclausal Deduction in First-Order Temporal Logic,” in Journal of the Association for Computing Machinery (JACM), Volume 37 (1990), Number 2 (April), pp. 279–317.Google Scholar
  2. [CES86]
    Clarke, E., Emerson, E., and Sistla, A.: “Automatic Verification of Finite-State Concurrent Systems Using Temporal Logic Specifications,” in ACM Transactions on Programming Languages and Systems, Volume 8 (1986), Number 2 (April), pp. 244–263.CrossRefGoogle Scholar
  3. [KM93]
    Kesten, Y., Manna, Z., McGuire, H., and Pnueli, A.: “A Decision Algorithm for Full Propositional Temporal Logic,” in Courcoubetis, C. (editor): Computer Aided Verification (5th International Conference, CAV '93) (LNCS #697), pp. 97–109. Springer-Verlag, Berlin, 1993.Google Scholar
  4. [MP91]
    Manna, Z., and Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag, New York, 1991.Google Scholar
  5. [MW80]
    Manna, Z., and Waldinger, R.: “A Deductive Approach to Program Synthesis,” in ACM Transactions on Programming Languages and Systems, Volume 2 (1980), pp. 90–121.CrossRefGoogle Scholar
  6. [MW93]
    Manna, Z., and Waldinger, R.: The Deductive Foundations of Computer Programming. Addison-Wesley, Reading, Massachusetts, 1993.Google Scholar
  7. [O88]
    Ohlbach, H.: “A Resolution Calculus for Modal Logics,” in Lusk, E., and Overbeek, R. (editors): 9th International Conference on Automated Deduction (Proceedings) (LNCS #310), pp. 500–516. Springer-Verlag, Berlin, 1988.Google Scholar
  8. [O93]
    Ohlbach, H.: “Translation Methods for Non-Classical Logics — An Overview,” in Automated Deduction in Nonstandard Logics (Technical Report #FS-93-01), pp. 113–125. AAAI Press, Menlo Park, California, 1993.Google Scholar
  9. [P86]
    Plaisted, D.: “A Decision Procedure for Combinations of Propositional Temporal Logic and Other Specialized Theories”, in Journal of Automated Reasoning, Volume 2 (1986), pp. 171–190.Google Scholar
  10. [S79]
    Shostak, R.: “A practical decision procedure for arithmetic with function symbols,” in JACM, Volume 26 (1979), Number 2 (April), pp. 351–360.CrossRefGoogle Scholar
  11. [W89]
    Wallen, L.: Automated Proof Search in Nonclassical Logics. The MIT Press, Cambridge, Massachusetts, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Hugh McGuire
    • 1
  • Zohar Manna
    • 1
  • Richard Waldinger
    • 2
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA
  2. 2.Artificial Intelligence CenterSRI InternationalMenlo ParkUSA

Personalised recommendations