Assume that ($\oplus$, $\otimes$) is a semiring over the positive reals.

If $\otimes$ is +, what are the possible operators for $\oplus$?


So far I have proven that `max`, `min`, and `softmax` (`logsumexp`) are solutions. Can we characterize all possible $\oplus$?


  [1]: https://en.wikipedia.org/wiki/Semiring#Specific_examples