Advertisement

The deducibility problem in Propositional Dynamic Logic

  • Albert R. Meyer
  • Robert S. Streett
  • Grazyna Mirkowska
Session 8: Z. Manna, Chairman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 115)

Abstract

The problem of whether an arbitrary formula of Propositional Dynamic Logic (PDL) is deducible from a fixed axiom scheme of PDL is Π 1 1 -complete. This contrasts with the decidability of the problem when the axiom scheme is replaced by any single PDL formula.

Keywords

Recursive Function Atomic Proposition Program Scheme Axiom Scheme Scheme Inference 
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.

References

  1. 1.
    Fischer, M. J. and R. E. Ladner, "Propositional Dynamic Logic of Regular Programs", JCSS, 18, 194–211, 1979.Google Scholar
  2. 2.
    Mirkowska, G., "Complete Axiomatization of Algorithmic Properties of Program Schemes with Bounded Nondeterministic Interpretations", Proceedings of the 12th ACM Symposium on Theory of Computing, 14–21, 1980.Google Scholar
  3. 3.
    Mirkowska, G., personal communication. Warsaw, July, 1980.Google Scholar
  4. 4.
    Pratt, V. R., "Models of Program Logics", JCSS, 20, 231–254, 1980.Google Scholar
  5. 5.
    Rogers, H., Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Company, 1967.Google Scholar
  6. 6.
    Shoenfield, J. R., Mathematical Logic, Addison-Wesley Publishing Company, 1967.Google Scholar
  7. 7.
    Streett, R. S., "Propositional Dynamic Logic of Looping and Converse", Proceedings of the 13th ACM Symposium on Theory of Computing, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Albert R. Meyer
    • 1
  • Robert S. Streett
    • 1
  • Grazyna Mirkowska
    • 2
  1. 1.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Institute of MathematicsWarsaw UniversityWarsawPoland

Personalised recommendations