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Dynamic Logic with Trace Semantics

  • Bernhard Beckert
  • Daniel Bruns
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7898)

Abstract

Dynamic logic is an established instrument for program verification and for reasoning about the semantics of programs and programming languages. In this paper, we define an extension of dynamic logic, called Dynamic Trace Logic (DTL), which combines the expressiveness of program logics such as dynamic logic with that of temporal logic. And we present a sound and relatively complete sequent calculus for proving validity of DTL formulae.

Due to its expressiveness, DTL can serve as a basis for proving functional and information-flow properties in concurrent programs, among other applications.

Keywords

Temporal Logic Trace Formula Linear Temporal Logic Logical Variable Variable Assignment 
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.

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References

  1. 1.
    Abadi, M., Manna, Z.: Nonclausal deduction in first-order temporal logic. Journal of the ACM 37(2), 279–317 (1990)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bauer, A., Leucker, M., Schallhart, C.: Comparing LTL semantics for runtime verification. J. Log. Comput. 20(3), 651–674 (2010)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Beckert, B.: A dynamic logic for Java Card. In: Proceedings, 2nd ECOOP Workshop on Formal Techniques for Java Programs, Cannes, France, pp. 111–119 (2000)Google Scholar
  4. 4.
    Beckert, B., Bruns, D.: Dynamic trace logic: Definition and proofs. Tech. Rep. 2012-10, Karlsruhe Institute of Technology, Department of Computer Science (2012), revised version available at http://formal.iti.kit.edu/~bruns/papers/trace-tr.pdf
  5. 5.
    Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334. Springer, Heidelberg (2007)Google Scholar
  6. 6.
    Beckert, B., Schlager, S.: A sequent calculus for first-order dynamic logic with trace modalities. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 626–641. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Goré, R.: Tableau methods for modal and temporal logics. In: D’Agostino, M., Gabbay, D., Hähnle, R., Posegga, J. (eds.) Handbook of Tableau Methods, pp. 297–396. Kluwer Academic Publishers, Dordrecht (1999)CrossRefGoogle Scholar
  8. 8.
    Harel, D.: Dynamic logic. In: Gabbay, D., Guenther, F. (eds.) Handbook of Philosophical Logic, Volume II: Extensions of Classical Logic, pp. 497–604. D. Reidel Publishing Co., Dordrecht (1984)CrossRefGoogle Scholar
  9. 9.
    Moszkowski, B.: A temporal logic for multilevel reasoning about hardware. IEEE Computer 18(2) (February 1985)Google Scholar
  10. 10.
    Platzer, A.: A temporal dynamic logic for verifying hybrid system invariants. In: Artemov, S., Nerode, A. (eds.) LFCS 2007. LNCS, vol. 4514, pp. 457–471. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Reynolds, M., Dixon, C.: Theorem-proving for discrete temporal logic. In: Fisher, D.M., Gabbay, Vila, L. (eds.) Handbook of Temporal Reasoning in Artificial Intelligence. Elsevier Science (2005)Google Scholar
  12. 12.
    Scheben, C., Schmitt, P.H.: Verification of information flow properties of java programs without approximations. In: Beckert, B., Damiani, F., Gurov, D. (eds.) FoVeOOS 2011. LNCS, vol. 7421, pp. 232–249. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Schellhorn, G., Tofan, B., Ernst, G., Reif, W.: Interleaved programs and rely-guarantee reasoning with ITL. In: Combi, C., Leucker, M., Wolter, F. (eds.) Eighteenth International Symposium on Temporal Representation and Reasoning, TIME 2011, pp. 99–106. IEEE (2011)Google Scholar
  14. 14.
    Thums, A., Schellhorn, G., Ortmeier, F., Reif, W.: Interactive verification of statecharts. In: Ehrig, H., Damm, W., Desel, J., Große-Rhode, M., Reif, W., Schnieder, E., Westkämper, E. (eds.) INT 2004. LNCS, vol. 3147, pp. 355–373. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Wolper, P.: The tableau method for temporal logic: An overview. Logique et Analyse 28(110-111), 119–136 (1985)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bernhard Beckert
    • 1
  • Daniel Bruns
    • 1
  1. 1.Karlsruhe Institute of Technology (KIT)Germany

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