It seems as if the consistency of logical propositions is amenable to being measured using cosine distance. let $\ell$ be such a metric.
For any proposition $P$, it is the case that $P$ is consistent with itself, so $\ell(P, P) = 1$
For any proposition $P$, it is the case that $P$ is not consistent with its negation, so $\ell(P, \neg P) = -1$.
However, it is additionally the case that a proposition $P$ and its negation $\neg P$ can be consistent with another set of logical statements. Let $P$ be the parallel postulate of euclidean geometry, and let $A_1, A_2, A_3, A_4$ be the remaining four axioms. Then it is the case that $\ell(P, A_i) = 0$. That is, one statement can be independent from another.
Surely some smarter mathematician saw this and created a way to measure the cosine distance of logical propositions. Who is that mathematician, and where can I find their papers?