Sorry to be rude, but could you ask/beg Prof Muggleton to write a book on ILP and/or meta-interpretive learning? Something like an expanded version of his outline webpage (https://www.doc.ic.ac.uk/~shm/ilp_theory.html).
My go-to for trying to understand ILP theory is Nienhuys-Cheng and de Wolf, _Foundations of Inductive Logic Programming_ and De Raedt's _Logical and Relational Learning_ is a more up-to-date overview, but I feel like there's room for a more modern textbook. This new MIL stuff seems to be be an important unifying idea that also connects back to abductive logic programming, if I understand correctly.
My go-to for trying to understand ILP theory is Nienhuys-Cheng and de Wolf, _Foundations of Inductive Logic Programming_ and De Raedt's _Logical and Relational Learning_ is a more up-to-date overview, but I feel like there's room for a more modern textbook. This new MIL stuff seems to be be an important unifying idea that also connects back to abductive logic programming, if I understand correctly.
Just a request; no offence intended!