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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.
The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The kno
This paper concerns the relation between process algebra and Hoare logic. We investigate the question whether and how a Hoare logic can be used for reasoning about how data change in the course of a process when reasoning equationally about that proc
We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction sequence concerne
Concolic testing is a popular dynamic validation technique that can be used for both model checking and automatic test case generation. We have recently introduced concolic testing in the context of logic programming. In contrast to previous approach
Coalition logic is one of the most popular logics for multi-agent systems. While epistemic extensions of coalition logic have received much attention, existence of their complete axiomatisations has so far been an open problem. In this paper we settl