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On the relative incompleteness of logics for total correctness

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Logics of Programs (Logic of Programs 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 193))

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Abstract

It is proved that it does not exist an acceptable /cf.4/ programming language having a sound and relatively complete /in the sense of Cook/ proof system for total correctness. This implies that the result of Clarke, German and Halpern concerning total correctness /cf.[4]/ cannot be essentially strengthened.

On the other hand, a chaim \(Q_0 \subseteq Q_1 \subseteq ... \subseteq Q_k \subseteq ...\) of classes of interpretations is defined such that for every kεω and every acceptable programming language with recursion there exists a proof system for total correctness, sound and complete over interpretations in Qk. For the class \(Q_\infty = \bigcup\limits_k {Q_k }\) /the class of all infinite expressive interpretations/ such system does not exist.

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References

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw PKiN p. 850, 00-901, Warszawa, POLAND

    Michał Grabowski

Authors
  1. Michał Grabowski
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Rohit Parikh

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© 1985 Springer-Verlag Berlin Heidelberg

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Grabowski, M. (1985). On the relative incompleteness of logics for total correctness. In: Parikh, R. (eds) Logics of Programs. Logic of Programs 1985. Lecture Notes in Computer Science, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15648-8_10

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  • DOI: https://doi.org/10.1007/3-540-15648-8_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15648-2

  • Online ISBN: 978-3-540-39527-0

  • eBook Packages: Springer Book Archive

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