> An analysis is sound if it reports all errors, and complete if it only reports errors.
This seems backwards. Soundness and completeness are terms from logic:
sound = every provable statement is true
complete = every true statement is provable
A statement is provable if and only if it can be derived within the system. For example, the statement "SS0 + SS0 = SSSS0" (i.e. 2+2=4) is provable in Peano Arithmetic (PA) because it can be derived from the axioms of PA.
By definition, a logical system that allows you to prove anything, even nonsense, is complete. Also, a logical system that doesn't allow you to prove anything is, by definition, sound.
In a comment at the bottom of the article, the author says:
> Soundness means: passed => not erroneous
> Completeness means: not erroneous => passed
>
> or equivalently, since rejected = (not passed):
>
> Soundness means: not rejected => not erroneous
> Completeness means: not erroneous => not rejected
This seems wrong. For one thing, rejected is not necessarily equivalent to not passed, because there is a third possibility: the algorithm might fail to terminate. This is analogous to a statement which can neither be proved nor disproved in a given logical system.
This article seems to confuse the concept of precision somewhat. Per Michael Hicks’ post on the same topic [1], precision is generally approaching soundness whereas recall or sensitivity is approaching completeness. Admittedly, I’ve also seen the term precision used far more loosely, including to describe approximate completeness (e.g. sound and precise).
sound = every provable statement is true
complete = every true statement is provable
A statement is provable if and only if it can be derived within the system. For example, the statement "SS0 + SS0 = SSSS0" (i.e. 2+2=4) is provable in Peano Arithmetic (PA) because it can be derived from the axioms of PA.
A statement is true if and only if it is actually true. For example, Goodstein's Theorem (https://en.wikipedia.org/wiki/Goodstein%27s_theorem) is true. However, Goodstein's Theorem is not provable in PA.
By definition, a logical system that allows you to prove anything, even nonsense, is complete. Also, a logical system that doesn't allow you to prove anything is, by definition, sound.
In a comment at the bottom of the article, the author says:
This seems wrong. For one thing, rejected is not necessarily equivalent to not passed, because there is a third possibility: the algorithm might fail to terminate. This is analogous to a statement which can neither be proved nor disproved in a given logical system.[1] (also cited in linked article) http://www.pl-enthusiast.net/2017/10/23/what-is-soundness-in...