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تسجيل مستخدم جديدOn Completeness Results of Hoare Logic Relative to the Standard Model
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The general completeness problem of Hoare logic relative to the standard model $N$ of Peano arithmetic has been studied by Cook, and it allows for the use of arbitrary arithmetical formulas as assertions. In practice, the assertions would be simple arithmetical formulas, e.g. of a low level in the arithmetical hierarchy. In addition, we find that, by restricting inputs to $N$, the complexity of the minimal assertion theory for the completeness of Hoare logic to hold can be reduced. This paper further studies the completeness of Hoare Logic relative to $N$ by restricting assertions to subclasses of arithmetical formulas (and by restricting inputs to $N$). Our completeness results refine Cooks result by reducing the complexity of the assertion theory.
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