Is ?some-other-time? sometimes better than ?sometime? for proving partial correctness of programs?

Abstract

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or “sometime”-logic. We will see that the minor change in this “background” modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the “reflexive version” of S5 with an “irreflexive version”, or intuitively as using the modality “some-other-time” instead of “sometime”. Some insights into the nature of computational induction and its variants are also obtained.