Logic of Programs 1985: Logics of Programs pp 118-127 | Cite as

On the relative incompleteness of logics for total correctness

Extended abstract
  • Michał Grabowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 193)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Michał Grabowski
    • 1
  1. 1.Institute of InformaticsUniversity of Warsaw PKiN p. 850WarszawaPOLAND

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