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Workshop on Logic of Programs

Logic of Programs 1979: Logic of Programs pp 12–22Cite as

The deducibility problem in propositional dynamic logic

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 125))

Abstract

The problem of whether an arbitrary formula of Propositional Dynamic Logic (PDL) is deducible from a fixed axiom scheme of PDL is Π 11 -complete. This contrasts with the decidability of the problem when the axiom scheme is replaced by any single PDL formula.

This research was supported in part by the National Science Foundation, grant nos. MCS 7719754, MCS 8010707, and MCS 7910261, and by a grant to the MIT Laboratory for Computer Science by the IBM Corporation.

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References

  1. Fischer, M. J. and R. E. Ladner, "Propositional Dynamic Logic of Regular Programs", JCSS, 18, 194–211, 1979.

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  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.

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  3. Mirkowska, G., personal communication. Warsaw, July, 1980.

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  4. Pratt, V. R., "Models of Program Logics", JCSS, 20, 231–254, 1980.

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  5. Rogers, H., Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Company, 1967.

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  6. Shoenfield, J. R., Mathematical Logic, Addison-Wesley Publishing Company, 1967.

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  7. Streett, R. S., "Propositional Dynamic Logic of Looping and Converse", Proceedings of the 13th ACM Symposium on Theory of Computing, 1981.

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Author information

Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Albert R. Meyer & Robert S. Streett

  2. Institute of Mathematics, Warsaw University, Warsaw, Poland

    Grazyna Mirkowska

Authors
  1. Albert R. Meyer
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  2. Robert S. Streett
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  3. Grazyna Mirkowska
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Editor information

Erwin Engeler

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© 1981 Springer-Verlag Berlin Heidelberg

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Meyer, A.R., Streett, R.S., Mirkowska, G. (1981). The deducibility problem in propositional dynamic logic. In: Engeler, E. (eds) Logic of Programs. Logic of Programs 1979. Lecture Notes in Computer Science, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11160-3_2

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  • DOI: https://doi.org/10.1007/3-540-11160-3_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11160-3

  • Online ISBN: 978-3-540-38631-5

  • eBook Packages: Springer Book Archive

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