On relative completeness of programming logics

Michal Grabowski
<span title="">1984</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2qaxtqe2rfgjnfefqcokcnzelq" style="color: black;">Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL &#39;84</a> </i> &nbsp;
In this paper a generalization of a certain Lipton's theorem (see Lipton [5] ) is presented. Namely,we show that for a wide class of programming languages the following holds:the set of all partial correctness assertions true in an expressive interpretation I is uniformly decidable (in I) in the theory of I iff the halting problem is decidable for finite interpretations. In the effect %~ show that such limitations as effectiveness or Herbrand definability of interpretation (they are relevant in
more &raquo; ... the previous proofs)can be removed in the case of partial correctness. B~CI~q~qOL~9 In this section we recall same history of the considered problem and we restate the known results. In order to show the inherent ccmple~(ity of the problem of partial correctness Cod~ introduced the notion of relative completeness. Supplying }~oare's system with an oracle answering questions on validity of first-order formulas he was able to separate the reasoning about the programs from the Permission to copy without fee all or part of this material is 8ranted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and.the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.
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