From a code modularization point of view, there shouldn’t really be much of a difference between programs and libraries. A program is just a library with a different calling convention. I like to structure programs such that their actual functionality could be reused as a library in another program.

This is difficult to reconcile with libraries only logging on a debug level.

I have a logging level I call "log lots" where it will log the first time with probability 1, but as it hits more often the same line, it will log with lower and lower probability bottoming out around 1/20000 times. Sort of a "log with probability proportional to the unlikiness of the event". So if I get e.g. sporadic failures to some back end, I will see them all, but if it goes down hard I will see it is still down but also be able to read other log msgs.

Why? Whats wrong with logging it and passing the log object to the caller? The caller can still modify the log entry however it pleases?

Eh, as with anything there are always exceptions. I generally agree with WARN and ERROR, though I can imagine a few situations where it might be appropriate for a library to log at those levels. Especially for a warning, like a library might emit "WARN Foo not available; falling back to Bar" on initialization, or something like that. And I think a library is fine logging at INFO (and DEBUG) as much as it wants.

Ultimately, though, it's important to be using a featureful logging framework (all the better if there's a "standard" one for your language or framework), so the end user can enable/disable different levels for different modules (including for your library).