Using hooks after logs are updated/created, fire off checks to see if a “rule” has been created for that circumstance
This would be pretty simple in a custom module. Not much code needed. Making it more flexible would be the challenging part… but…
There’s a module for that! And it’s called “Rules”! 
I’ve held off including it in farmOS for a couple of reasons, but I’ve always thought it could be a really useful tool, especially for advanced users. It let’s you configure “rules” via the UI, that happen on specific “events/triggers”, are limited by “conditions”, and then execute specific “actions”.
It’s low-hanging fruit for someone who is hosting farmOS themselves to drop in and play around with.
One of the biggest reasons I haven’t added it “officially” to farmOS is that the Drupal 8 upgrade path has been a question mark. I haven’t looked at it in a while, though, so maybe worth investigating. I think Rules was being refactored from the ground up for Drupal 8, so I figured we’d just wait until we’re on D8 to look at it again. I don’t know if a D7->D8 migration path is being worked on.
So in summary: Rules would make it really easy for advanced farmOS users (but not necessarily programmers) to configure triggered actions in the UI. But if you are comfortable with a bit of programming, writing a custom module to do exactly what you want might be simpler (and provide more options).