Is there a possible intersection of mathematical logic and machine learning?
I think the reason why formal logic is not widely used is its strictness. Also, it has quite restricted area of application and requires the domain to be formalized first. In contrast to that, ML methods can be fuzzy, robust to noise and work well for real-life data.

Here is an interesting discussion on the topic:
https://www.quora.com/Whats-the-relationship-between-mathematical-Logic-and-Machine-Learning