Expressiveness and the completeness of Hoare's logic

https://doi.org/10.1016/0022-0000(82)90013-7Get rights and content
Under an Elsevier user license
open archive

Abstract

Three theorems are proven which reconsider the completeness of Hoare's logic for the partial correctness of while-programs equipped with a first-order assertion language. The results are about the expressiveness of the assertion language and the role of specifications in completeness concerns for the logic: (1) expressiveness is not a necessary condition on a structure for its Hoare logic to be complete, (2) complete number theory is the only extension of Peano Arithmetic which yields a logically complete Hoare logic and (3) a computable structure with enumeration is expressive if and only if its Hoare logic is complete.

Cited by (0)

The results in this paper were obtained while the second author was at the Mathematical Centre, Amsterdam, and an earlier edition of this paper is registered there as MC Report IW 149/80.