Is there a system that automatically designs a set of rules from the examples? Being by no means an expert in the field, I do however know of solvers such as Z3 that can generate a correct program, provided you can express your constraints as a set of logical rules, such as here.
However, in the example given above, logical rules are designed &quot;by hand&quot; from a set of examples, so the &quot;compilation step&quot; from the examples to the set of rules must be done in the user's head.
Does a system automating this &quot;compilation step&quot; exist (i.e automated rule set deduction from a set of examples), that would allow the user to see and make use of the set of rules?
This is an active research topic.
Consider reading

J.Pitrat's Artificial Beings, the conscience of a conscious machine book

This Understanding machine learning book

old Lenat's papers on Eurisko.

and recent papers such as Learning Structured Embeddings of Knowledge Bases and several others in Artificial Intelligence Journal

about the MILEPOST GCC and Ctuning projects

this paper on Reconciling deep learning with symbolic artificial intelligence: representing objects and relations


My hope is to get funded so that RefPerSys could (in a few years) be able to deduce some rules and metarules.