On the completeness of propositional Hoare logic

On the Completeness of Propositional Hoare Logic

As shown by Cook [5], Hoare logic is relatively complete for partial correctness assertions (PCAs) over while programs whenever the underlying assertion language is sufficiently expressive. The expressiveness conditions in Cook’s formulation provide for the expression of weakest preconditions. These conditions holds for first-order logic over , for example, because of the coding power of first-...

Completeness of Hoare Logic over Nonstandard Models

The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The known versions of nonstandard semantics, the Hungary semantics and axiomatic semantics, are so general that they are absent either from mathematical elegance or from practical usefulness. The aim of this paper is to exhibit a not only mathematically elegant but also practic...

The completeness of Stoic propositional logic

On the polynomial-space completeness of intuitionistic propositional logic

We present an alternative, purely semantical and relatively simple, proof of the Statman’s result that both intuitionistic propositional logic and its implicational fragment are PSPACE -complete.

Hoare logic and VDM : machine-checked soundness and completeness proofs

Investigating soundness and completeness of verification calculi for imperative programming languages is a challenging task. Many incorrect results have been published in the past. We take advantage of the computer-aided proof tool LEGO to interactively establish soundness and completeness of both Hoare Logic and the operation decomposition rules of the Vienna Development Method (VDM) with resp...