[Cladode]

This comment is deeply misleading. O'Hearn's incorrectness logic that you cite in your [1] is perfectly sound. It just changes the meaning of Hoare triples from over-approximation to under-approximation. In brief:

- Hoare logic soundly over-approximates

- Incorrectness logic soundly under-approximates

Sound under-approximation is extremely useful when you want to prove that a certain problem must arise in code, rather than may arise. The problem with logic based program verification has often been that your prover could not prove that a program was correct, but, due to over-approximation of traditional Hoare logic, the best you could learn from this failure was (simplifying a great deal) that something may go wrong. That is not particularly useful in practise, since often this is a false alert.

[pron]

I am well aware. In software verification, a "sound" verification method usually means no missed bugs. Obviously, the logic is sound in the sense that it cannot be used to prove false statements; in that same sense, tests are also sound, and yet in software verification, tests are considered an unsound verification technique (which, these days, is becoming good).

[Cladode]

Tests are not sound in the sense of conventional program logic (overapproximation). O'Hearn's [1] even proves a soundness theorem. So when you say say [1] is not sound then this is confusing for the reader.

[pron]

> Tests are not sound in the sense of conventional program logic (overapproximation).

Of course they are, in the logic sense of "sound", and in the same sense that incorrectness logic is sound. A test is a proof of a proposition about a single program behavior (provided that the execution is deterministic). But neither testing nor incorrectness logic are sound in the sense that term is used in software verification, namely as proofs of some explicit or implied universal proposition. In software verification, a sound technique is one that guarantees conformance to a specification over all behaviors (or conversely, the absence of spec violations in any behavior).

[Cladode]

   In software verification, 
   a sound technique is ...

In other words, tests are not sound ... Anyway, we are quibbling about meaning of words, so this is unlikely to be fruitful.