Another incompleteness result for Hoare's logic

It is known (Bergstra and Tucker (1982) J. Comput. System Sci. 25, 217) that if the Hoare rules are complete for a first-order structure %plane1D;49C;, then the set of partial correctness assertions true over %plane1D;49C; is recursive in the first-order theory of %plane1D;49C;. We show that the converse is not true. Namely, there is a first-order structure %plane1D;49E; such that the set of partial correctness assertions true over %plane1D;49E; is recursive in the theory of %plane1D;49E;, but the Hoare rules are not complete for %plane1D;49E;

Relative completeness of a Hoare-calculus for while-programs

In several papers,e.g. [COOK] or [APT] the problems of correctness and completeness of Hoare calculi have been studied. The purpose of this paper is to present a simple approach to this subject by restricting the attention to a very small class of programs, the so-called while-programs

Some general incompleteness results for partial correctness logics

AbstractIt is known that incompleteness of Hoare's logic relative to certain data type specifications can occur due to the ability of partial correctness assertions to code unsolvable problems; cf. Andréka, Németi, and Sain (1979, Lecture Notes in Computer Science Vol. 74, pp. 208–218, Springer-Verlag, New York/Berlin) and Bergstra and Tucker (1982, Theoret. Comput. Sci. 17, 303–315). We improve what we think are the main known theorems of this kind, showing that they depend only on very weak assumptions on the data type specification (ensuring the ability to simulate arbitrarily long finite initial segments of the natural numbers with successor), and pointing out that the recursion theoretic strength of the obtained results can be increased

Relative completeness of a Hoare-calculus for while-programs

In several papers,e.g. [COOK] or [APT] the problems of correctness and completeness of Hoare calculi have been studied. The purpose of this paper is to present a simple approach to this subject by restricting the attention to a very small class of programs, the so-called while-programs