Learnability of an Oracle

Stream: general

[Koundinya Vajjha]

Say I have an oracle in my vicinity which answers well-formed queries I pose to it in some language $L$. For my application, I am assuming it to be a proof-checker kernel.

1. I am interested in analogues of Angluin's algorithm for learning the logic of the proof-checker (or equivalently, the language $L$).
2. Say I generate queries randomly and ask the oracle, what proportion (read measure) of the queries can one expect to be positively answered?

Apologies if these questions are vague, I've only just read about this a few hours ago and was curious what the community has to say about them.