Does somebody know a logic with some modal operator $\sim$, where a degree of inconsistency between two statements $\sim ( \phi(x) = a ) $ and $\sim( \phi(x) = b) $ is a monotonous function $f: |a - b| \rightarrow R^+, \; f(0) = 0$?
The modal operator $\sim$ may be interpreted as "It appears". The logic would be great to formalize machine learning.
Would you have objections against such logic if it is proposed?